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<div class="title">Eigen_Colamd.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// // This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2012 Desire Nuentsa Wakam &lt;desire.nuentsa_wakam@inria.fr&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">// This file is modified from the colamd/symamd library. The copyright is below</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160; </div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">//   The authors of the code itself are Stefan I. Larimore and Timothy A.</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">//   Davis (davis@cise.ufl.edu), University of Florida.  The algorithm was</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">//   developed in collaboration with John Gilbert, Xerox PARC, and Esmond</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">//   Ng, Oak Ridge National Laboratory.</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment">//     Date:</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">//   September 8, 2003.  Version 2.3.</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment">//     Acknowledgements:</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="comment">//   This work was supported by the National Science Foundation, under</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="comment">//   grants DMS-9504974 and DMS-9803599.</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment">//     Notice:</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="comment">//   Copyright (c) 1998-2003 by the University of Florida.</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="comment">//   All Rights Reserved.</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="comment">//   THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="comment">//   EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.</span></div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="comment">//   Permission is hereby granted to use, copy, modify, and/or distribute</span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="comment">//   this program, provided that the Copyright, this License, and the</span></div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="comment">//   Availability of the original version is retained on all copies and made</span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="comment">//   accessible to the end-user of any code or package that includes COLAMD</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="comment">//   or any modified version of COLAMD.</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="comment">//     Availability:</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="comment">//   The colamd/symamd library is available at</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;<span class="comment">//       http://www.suitesparse.com</span></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160; </div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160; </div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="preprocessor">#ifndef EIGEN_COLAMD_H</span></div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;<span class="preprocessor">#define EIGEN_COLAMD_H</span></div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160; </div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="keyword">namespace </span>Colamd {</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160; </div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="comment">/* Ensure that debugging is turned off: */</span></div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;<span class="preprocessor">#ifndef COLAMD_NDEBUG</span></div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;<span class="preprocessor">#define COLAMD_NDEBUG</span></div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;<span class="preprocessor">#endif </span><span class="comment">/* NDEBUG */</span><span class="preprocessor"></span></div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160; </div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160; </div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;<span class="comment">/* === Knob and statistics definitions ====================================== */</span></div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160; </div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;<span class="comment">/* size of the knobs [ ] array.  Only knobs [0..1] are currently used. */</span></div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;<span class="keyword">const</span> <span class="keywordtype">int</span> NKnobs = 20;</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160; </div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="comment">/* number of output statistics.  Only stats [0..6] are currently used. */</span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;<span class="keyword">const</span> <span class="keywordtype">int</span> NStats = 20;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160; </div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="comment">/* Indices into knobs and stats array. */</span></div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="keyword">enum</span> KnobsStatsIndex {</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;  <span class="comment">/* knobs [0] and stats [0]: dense row knob and output statistic. */</span></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;  DenseRow = 0,</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160; </div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  <span class="comment">/* knobs [1] and stats [1]: dense column knob and output statistic. */</span></div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  DenseCol = 1,</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160; </div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;  <span class="comment">/* stats [2]: memory defragmentation count output statistic */</span></div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  DefragCount = 2,</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160; </div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;  <span class="comment">/* stats [3]: colamd status:  zero OK, &gt; 0 warning or notice, &lt; 0 error */</span></div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  Status = 3,</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160; </div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;  <span class="comment">/* stats [4..6]: error info, or info on jumbled columns */</span></div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;  Info1 = 4,</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  Info2 = 5,</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;  Info3 = 6</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;};</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160; </div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;<span class="comment">/* error codes returned in stats [3]: */</span></div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;<span class="keyword">enum</span> Status {</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  Ok = 0,</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  OkButJumbled = 1,</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  ErrorANotPresent = -1,</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;  ErrorPNotPresent = -2,</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  ErrorNrowNegative = -3,</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;  ErrorNcolNegative = -4,</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;  ErrorNnzNegative = -5,</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  ErrorP0Nonzero = -6,</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  ErrorATooSmall = -7,</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;  ErrorColLengthNegative = -8,</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;  ErrorRowIndexOutOfBounds = -9,</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;  ErrorOutOfMemory = -10,</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;  ErrorInternalError = -999</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;};</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;<span class="comment">/* === Definitions ========================================================== */</span></div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160; </div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;IndexType ones_complement(<span class="keyword">const</span> IndexType r) {</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  <span class="keywordflow">return</span> (-(r)-1);</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;}</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160; </div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;<span class="comment">/* -------------------------------------------------------------------------- */</span></div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;<span class="keyword">const</span> <span class="keywordtype">int</span> Empty = -1;</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160; </div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;<span class="comment">/* Row and column status */</span></div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;<span class="keyword">enum</span> RowColumnStatus {</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;  Alive = 0,</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;  Dead = -1</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;};</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160; </div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;<span class="comment">/* Column status */</span></div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="keyword">enum</span> ColumnStatus {</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  DeadPrincipal = -1,</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;  DeadNonPrincipal = -2</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;};</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160; </div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;<span class="comment">/* === Colamd reporting mechanism =========================================== */</span></div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160; </div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="comment">// == Row and Column structures ==</span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;<span class="keyword">struct </span>ColStructure</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;{</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;  IndexType start ;   <span class="comment">/* index for A of first row in this column, or Dead */</span></div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;  <span class="comment">/* if column is dead */</span></div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;  IndexType length ;  <span class="comment">/* number of rows in this column */</span></div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;  <span class="keyword">union</span></div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;  {</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    IndexType thickness ; <span class="comment">/* number of original columns represented by this */</span></div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;    <span class="comment">/* col, if the column is alive */</span></div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    IndexType parent ;  <span class="comment">/* parent in parent tree super-column structure, if */</span></div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    <span class="comment">/* the column is dead */</span></div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  } shared1 ;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;  <span class="keyword">union</span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;  {</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    IndexType score ; <span class="comment">/* the score used to maintain heap, if col is alive */</span></div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;    IndexType order ; <span class="comment">/* pivot ordering of this column, if col is dead */</span></div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;  } shared2 ;</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;  <span class="keyword">union</span></div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;  {</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;    IndexType headhash ;  <span class="comment">/* head of a hash bucket, if col is at the head of */</span></div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;    <span class="comment">/* a degree list */</span></div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    IndexType hash ;  <span class="comment">/* hash value, if col is not in a degree list */</span></div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;    IndexType prev ;  <span class="comment">/* previous column in degree list, if col is in a */</span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <span class="comment">/* degree list (but not at the head of a degree list) */</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;  } shared3 ;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;  <span class="keyword">union</span></div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;  {</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;    IndexType degree_next ; <span class="comment">/* next column, if col is in a degree list */</span></div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;    IndexType hash_next ;   <span class="comment">/* next column, if col is in a hash list */</span></div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  } shared4 ;</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160; </div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">bool</span> is_dead()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> start &lt; Alive; }</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160; </div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">bool</span> is_alive()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> start &gt;= Alive; }</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160; </div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">bool</span> is_dead_principal()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> start == DeadPrincipal; }</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160; </div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">void</span> kill_principal() { start = DeadPrincipal; }</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160; </div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">void</span> kill_non_principal() { start = DeadNonPrincipal; }</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160; </div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;};</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160; </div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;<span class="keyword">struct </span>RowStructure</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;{</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;  IndexType start ;   <span class="comment">/* index for A of first col in this row */</span></div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;  IndexType length ;  <span class="comment">/* number of principal columns in this row */</span></div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  <span class="keyword">union</span></div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;  {</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;    IndexType degree ;  <span class="comment">/* number of principal &amp; non-principal columns in row */</span></div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;    IndexType p ;   <span class="comment">/* used as a row pointer in init_rows_cols () */</span></div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;  } shared1 ;</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;  <span class="keyword">union</span></div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;  {</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    IndexType mark ;  <span class="comment">/* for computing set differences and marking dead rows*/</span></div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    IndexType first_column ;<span class="comment">/* first column in row (used in garbage collection) */</span></div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;  } shared2 ;</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160; </div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">bool</span> is_dead()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> shared2.mark &lt; Alive; }</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160; </div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">bool</span> is_alive()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> shared2.mark &gt;= Alive; }</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160; </div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">void</span> kill() { shared2.mark = Dead; }</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160; </div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;};</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160; </div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;<span class="comment">/* === Colamd recommended memory size ======================================= */</span></div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160; </div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;<span class="comment">  The recommended length Alen of the array A passed to colamd is given by</span></div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;<span class="comment">  the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro.  It returns -1 if any</span></div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;<span class="comment">  argument is negative.  2*nnz space is required for the row and column</span></div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;<span class="comment">  indices of the matrix. colamd_c (n_col) + colamd_r (n_row) space is</span></div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;<span class="comment">  required for the Col and Row arrays, respectively, which are internal to</span></div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;<span class="comment">  colamd.  An additional n_col space is the minimal amount of &quot;elbow room&quot;,</span></div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;<span class="comment">  and nnz/5 more space is recommended for run time efficiency.</span></div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;<span class="comment">  This macro is not needed when using symamd.</span></div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;<span class="comment">  Explicit typecast to IndexType added Sept. 23, 2002, COLAMD version 2.2, to avoid</span></div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;<span class="comment">  gcc -pedantic warning messages.</span></div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;<span class="keyword">inline</span> IndexType colamd_c(IndexType n_col)</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;{ <span class="keywordflow">return</span> IndexType( ((n_col) + 1) * <span class="keyword">sizeof</span> (ColStructure&lt;IndexType&gt;) / <span class="keyword">sizeof</span> (IndexType) ) ; }</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160; </div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;<span class="keyword">inline</span> IndexType  colamd_r(IndexType n_row)</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;{ <span class="keywordflow">return</span> IndexType(((n_row) + 1) * <span class="keyword">sizeof</span> (RowStructure&lt;IndexType&gt;) / <span class="keyword">sizeof</span> (IndexType)); }</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160; </div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;<span class="comment">// Prototypes of non-user callable routines</span></div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;<span class="keyword">static</span> IndexType init_rows_cols (IndexType n_row, IndexType n_col, RowStructure&lt;IndexType&gt; Row [], ColStructure&lt;IndexType&gt; col [], IndexType A [], IndexType p [], IndexType stats[NStats] );</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160; </div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;<span class="keyword">static</span> <span class="keywordtype">void</span> init_scoring (IndexType n_row, IndexType n_col, RowStructure&lt;IndexType&gt; Row [], ColStructure&lt;IndexType&gt; Col [], IndexType A [], IndexType head [], <span class="keywordtype">double</span> knobs[NKnobs], IndexType *p_n_row2, IndexType *p_n_col2, IndexType *p_max_deg);</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160; </div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;<span class="keyword">static</span> IndexType find_ordering (IndexType n_row, IndexType n_col, IndexType Alen, RowStructure&lt;IndexType&gt; Row [], ColStructure&lt;IndexType&gt; Col [], IndexType A [], IndexType head [], IndexType n_col2, IndexType max_deg, IndexType pfree);</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160; </div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;<span class="keyword">static</span> <span class="keywordtype">void</span> order_children (IndexType n_col, ColStructure&lt;IndexType&gt; Col [], IndexType p []);</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160; </div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;<span class="keyword">static</span> <span class="keywordtype">void</span> detect_super_cols (ColStructure&lt;IndexType&gt; Col [], IndexType A [], IndexType head [], IndexType row_start, IndexType row_length ) ;</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160; </div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;<span class="keyword">static</span> IndexType garbage_collection (IndexType n_row, IndexType n_col, RowStructure&lt;IndexType&gt; Row [], ColStructure&lt;IndexType&gt; Col [], IndexType A [], IndexType *pfree) ;</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160; </div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;<span class="keyword">static</span> <span class="keyword">inline</span>  IndexType clear_mark (IndexType n_row, RowStructure&lt;IndexType&gt; Row [] ) ;</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160; </div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;<span class="comment">/* === No debugging ========================================================= */</span></div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160; </div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;<span class="preprocessor">#define COLAMD_DEBUG0(params) ;</span></div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;<span class="preprocessor">#define COLAMD_DEBUG1(params) ;</span></div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;<span class="preprocessor">#define COLAMD_DEBUG2(params) ;</span></div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;<span class="preprocessor">#define COLAMD_DEBUG3(params) ;</span></div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;<span class="preprocessor">#define COLAMD_DEBUG4(params) ;</span></div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160; </div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;<span class="preprocessor">#define COLAMD_ASSERT(expression) ((void) 0)</span></div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160; </div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160; </div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;<span class="keyword">inline</span> IndexType recommended ( IndexType nnz, IndexType n_row, IndexType n_col)</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;{</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;  <span class="keywordflow">if</span> ((nnz) &lt; 0 || (n_row) &lt; 0 || (n_col) &lt; 0)</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;    <span class="keywordflow">return</span> (-1);</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;    <span class="keywordflow">return</span> (2 * (nnz) + colamd_c (n_col) + colamd_r (n_row) + (n_col) + ((nnz) / 5));</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;}</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160; </div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;<span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> set_defaults(<span class="keywordtype">double</span> knobs[NKnobs])</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;{</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160; </div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;  <span class="keywordtype">int</span> i ;</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160; </div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;  <span class="keywordflow">if</span> (!knobs)</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;  {</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;    return ;      <span class="comment">/* no knobs to initialize */</span></div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;  }</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;  <span class="keywordflow">for</span> (i = 0 ; i &lt; NKnobs ; i++)</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;  {</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;    knobs [i] = 0 ;</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;  }</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;  knobs [Colamd::DenseRow] = 0.5 ;  <span class="comment">/* ignore rows over 50% dense */</span></div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;  knobs [Colamd::DenseCol] = 0.5 ;  <span class="comment">/* ignore columns over 50% dense */</span></div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;}</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160; </div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;<span class="keyword">static</span> <span class="keywordtype">bool</span> compute_ordering(IndexType n_row, IndexType n_col, IndexType Alen, IndexType *A, IndexType *p, <span class="keywordtype">double</span> knobs[NKnobs], IndexType stats[NStats])</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;{</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160; </div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;  IndexType i ;     <span class="comment">/* loop index */</span></div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;  IndexType nnz ;     <span class="comment">/* nonzeros in A */</span></div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;  IndexType Row_size ;    <span class="comment">/* size of Row [], in integers */</span></div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;  IndexType Col_size ;    <span class="comment">/* size of Col [], in integers */</span></div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;  IndexType need ;      <span class="comment">/* minimum required length of A */</span></div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;  Colamd::RowStructure&lt;IndexType&gt; *Row ;   <span class="comment">/* pointer into A of Row [0..n_row] array */</span></div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;  Colamd::ColStructure&lt;IndexType&gt; *Col ;   <span class="comment">/* pointer into A of Col [0..n_col] array */</span></div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;  IndexType n_col2 ;    <span class="comment">/* number of non-dense, non-empty columns */</span></div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;  IndexType n_row2 ;    <span class="comment">/* number of non-dense, non-empty rows */</span></div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;  IndexType ngarbage ;    <span class="comment">/* number of garbage collections performed */</span></div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;  IndexType max_deg ;   <span class="comment">/* maximum row degree */</span></div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;  <span class="keywordtype">double</span> default_knobs [NKnobs] ; <span class="comment">/* default knobs array */</span></div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160; </div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160; </div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;  <span class="comment">/* === Check the input arguments ======================================== */</span></div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160; </div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;  <span class="keywordflow">if</span> (!stats)</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;  {</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;    COLAMD_DEBUG0 ((<span class="stringliteral">&quot;colamd: stats not present\n&quot;</span>)) ;</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;  }</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;  <span class="keywordflow">for</span> (i = 0 ; i &lt; NStats ; i++)</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;  {</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;    stats [i] = 0 ;</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;  }</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;  stats [Colamd::Status] = Colamd::Ok ;</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;  stats [Colamd::Info1] = -1 ;</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;  stats [Colamd::Info2] = -1 ;</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160; </div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;  <span class="keywordflow">if</span> (!A)   <span class="comment">/* A is not present */</span></div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;  {</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;    stats [Colamd::Status] = Colamd::ErrorANotPresent ;</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;    COLAMD_DEBUG0 ((<span class="stringliteral">&quot;colamd: A not present\n&quot;</span>)) ;</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;  }</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160; </div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;  <span class="keywordflow">if</span> (!p)   <span class="comment">/* p is not present */</span></div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;  {</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;    stats [Colamd::Status] = Colamd::ErrorPNotPresent ;</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;    COLAMD_DEBUG0 ((<span class="stringliteral">&quot;colamd: p not present\n&quot;</span>)) ;</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;  }</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160; </div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;  <span class="keywordflow">if</span> (n_row &lt; 0)  <span class="comment">/* n_row must be &gt;= 0 */</span></div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;  {</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;    stats [Colamd::Status] = Colamd::ErrorNrowNegative ;</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;    stats [Colamd::Info1] = n_row ;</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;    COLAMD_DEBUG0 ((<span class="stringliteral">&quot;colamd: nrow negative %d\n&quot;</span>, n_row)) ;</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;  }</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160; </div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;  <span class="keywordflow">if</span> (n_col &lt; 0)  <span class="comment">/* n_col must be &gt;= 0 */</span></div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;  {</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;    stats [Colamd::Status] = Colamd::ErrorNcolNegative ;</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;    stats [Colamd::Info1] = n_col ;</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;    COLAMD_DEBUG0 ((<span class="stringliteral">&quot;colamd: ncol negative %d\n&quot;</span>, n_col)) ;</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;  }</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160; </div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;  nnz = p [n_col] ;</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;  <span class="keywordflow">if</span> (nnz &lt; 0)  <span class="comment">/* nnz must be &gt;= 0 */</span></div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;  {</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;    stats [Colamd::Status] = Colamd::ErrorNnzNegative ;</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;    stats [Colamd::Info1] = nnz ;</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;    COLAMD_DEBUG0 ((<span class="stringliteral">&quot;colamd: number of entries negative %d\n&quot;</span>, nnz)) ;</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;  }</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160; </div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;  <span class="keywordflow">if</span> (p [0] != 0)</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;  {</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;    stats [Colamd::Status] = Colamd::ErrorP0Nonzero ;</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;    stats [Colamd::Info1] = p [0] ;</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;    COLAMD_DEBUG0 ((<span class="stringliteral">&quot;colamd: p[0] not zero %d\n&quot;</span>, p [0])) ;</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;  }</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160; </div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;  <span class="comment">/* === If no knobs, set default knobs =================================== */</span></div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160; </div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;  <span class="keywordflow">if</span> (!knobs)</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;  {</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;    set_defaults (default_knobs) ;</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;    knobs = default_knobs ;</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;  }</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160; </div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;  <span class="comment">/* === Allocate the Row and Col arrays from array A ===================== */</span></div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160; </div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;  Col_size = colamd_c (n_col) ;</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;  Row_size = colamd_r (n_row) ;</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;  need = 2*nnz + n_col + Col_size + Row_size ;</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160; </div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;  <span class="keywordflow">if</span> (need &gt; Alen)</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;  {</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;    <span class="comment">/* not enough space in array A to perform the ordering */</span></div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;    stats [Colamd::Status] = Colamd::ErrorATooSmall ;</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;    stats [Colamd::Info1] = need ;</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;    stats [Colamd::Info2] = Alen ;</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;    COLAMD_DEBUG0 ((<span class="stringliteral">&quot;colamd: Need Alen &gt;= %d, given only Alen = %d\n&quot;</span>, need,Alen));</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;  }</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160; </div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;  Alen -= Col_size + Row_size ;</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;  Col = (ColStructure&lt;IndexType&gt; *) &amp;A [Alen] ;</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;  Row = (RowStructure&lt;IndexType&gt; *) &amp;A [Alen + Col_size] ;</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160; </div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;  <span class="comment">/* === Construct the row and column data structures ===================== */</span></div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160; </div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;  <span class="keywordflow">if</span> (!Colamd::init_rows_cols (n_row, n_col, Row, Col, A, p, stats))</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;  {</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;    <span class="comment">/* input matrix is invalid */</span></div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;    COLAMD_DEBUG0 ((<span class="stringliteral">&quot;colamd: Matrix invalid\n&quot;</span>)) ;</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;  }</div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160; </div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;  <span class="comment">/* === Initialize scores, kill dense rows/columns ======================= */</span></div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160; </div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;  Colamd::init_scoring (n_row, n_col, Row, Col, A, p, knobs,</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;                &amp;n_row2, &amp;n_col2, &amp;max_deg) ;</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160; </div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;  <span class="comment">/* === Order the supercolumns =========================================== */</span></div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160; </div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;  ngarbage = Colamd::find_ordering (n_row, n_col, Alen, Row, Col, A, p,</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;                            n_col2, max_deg, 2*nnz) ;</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160; </div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;  <span class="comment">/* === Order the non-principal columns ================================== */</span></div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160; </div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;  Colamd::order_children (n_col, Col, p) ;</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160; </div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;  <span class="comment">/* === Return statistics in stats ======================================= */</span></div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160; </div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;  stats [Colamd::DenseRow] = n_row - n_row2 ;</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;  stats [Colamd::DenseCol] = n_col - n_col2 ;</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;  stats [Colamd::DefragCount] = ngarbage ;</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;  COLAMD_DEBUG0 ((<span class="stringliteral">&quot;colamd: done.\n&quot;</span>)) ;</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;  <span class="keywordflow">return</span> (<span class="keyword">true</span>) ;</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;}</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160; </div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;<span class="comment">/* === NON-USER-CALLABLE ROUTINES: ========================================== */</span></div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160; </div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;<span class="comment">/* There are no user-callable routines beyond this point in the file */</span></div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160; </div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;<span class="comment">/* === init_rows_cols ======================================================= */</span></div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160; </div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;<span class="comment">  Takes the column form of the matrix in A and creates the row form of the</span></div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;<span class="comment">  matrix.  Also, row and column attributes are stored in the Col and Row</span></div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;<span class="comment">  structs.  If the columns are un-sorted or contain duplicate row indices,</span></div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;<span class="comment">  this routine will also sort and remove duplicate row indices from the</span></div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;<span class="comment">  column form of the matrix.  Returns false if the matrix is invalid,</span></div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;<span class="comment">  true otherwise.  Not user-callable.</span></div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;<span class="keyword">static</span> IndexType init_rows_cols  <span class="comment">/* returns true if OK, or false otherwise */</span></div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;  (</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;    <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160; </div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;    IndexType n_row,      <span class="comment">/* number of rows of A */</span></div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;    IndexType n_col,      <span class="comment">/* number of columns of A */</span></div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;    RowStructure&lt;IndexType&gt; Row [],    <span class="comment">/* of size n_row+1 */</span></div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;    ColStructure&lt;IndexType&gt; Col [],    <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;    IndexType A [],     <span class="comment">/* row indices of A, of size Alen */</span></div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;    IndexType p [],     <span class="comment">/* pointers to columns in A, of size n_col+1 */</span></div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;    IndexType stats [NStats]  <span class="comment">/* colamd statistics */</span></div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;    )</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;{</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160; </div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;  IndexType col ;     <span class="comment">/* a column index */</span></div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;  IndexType row ;     <span class="comment">/* a row index */</span></div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;  IndexType *cp ;     <span class="comment">/* a column pointer */</span></div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;  IndexType *cp_end ;   <span class="comment">/* a pointer to the end of a column */</span></div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;  IndexType *rp ;     <span class="comment">/* a row pointer */</span></div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;  IndexType *rp_end ;   <span class="comment">/* a pointer to the end of a row */</span></div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;  IndexType last_row ;    <span class="comment">/* previous row */</span></div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160; </div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;  <span class="comment">/* === Initialize columns, and check column pointers ==================== */</span></div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160; </div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;  <span class="keywordflow">for</span> (col = 0 ; col &lt; n_col ; col++)</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;  {</div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;    Col [col].start = p [col] ;</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;    Col [col].length = p [col+1] - p [col] ;</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160; </div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;    <span class="keywordflow">if</span> ((Col [col].length) &lt; 0) <span class="comment">// extra parentheses to work-around gcc bug 10200</span></div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;    {</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;      <span class="comment">/* column pointers must be non-decreasing */</span></div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;      stats [Colamd::Status] = Colamd::ErrorColLengthNegative ;</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;      stats [Colamd::Info1] = col ;</div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;      stats [Colamd::Info2] = Col [col].length ;</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;      COLAMD_DEBUG0 ((<span class="stringliteral">&quot;colamd: col %d length %d &lt; 0\n&quot;</span>, col, Col [col].length)) ;</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;      <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;    }</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160; </div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;    Col [col].shared1.thickness = 1 ;</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;    Col [col].shared2.score = 0 ;</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;    Col [col].shared3.prev = Empty ;</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;    Col [col].shared4.degree_next = Empty ;</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;  }</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160; </div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;  <span class="comment">/* p [0..n_col] no longer needed, used as &quot;head&quot; in subsequent routines */</span></div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160; </div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;  <span class="comment">/* === Scan columns, compute row degrees, and check row indices ========= */</span></div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160; </div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;  stats [Info3] = 0 ;  <span class="comment">/* number of duplicate or unsorted row indices*/</span></div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160; </div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;  <span class="keywordflow">for</span> (row = 0 ; row &lt; n_row ; row++)</div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;  {</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;    Row [row].length = 0 ;</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;    Row [row].shared2.mark = -1 ;</div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;  }</div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160; </div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;  <span class="keywordflow">for</span> (col = 0 ; col &lt; n_col ; col++)</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;  {</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;    last_row = -1 ;</div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160; </div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;    cp = &amp;A [p [col]] ;</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;    cp_end = &amp;A [p [col+1]] ;</div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160; </div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;    <span class="keywordflow">while</span> (cp &lt; cp_end)</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;    {</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;      row = *cp++ ;</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160; </div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;      <span class="comment">/* make sure row indices within range */</span></div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;      <span class="keywordflow">if</span> (row &lt; 0 || row &gt;= n_row)</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;      {</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;        stats [Colamd::Status] = Colamd::ErrorRowIndexOutOfBounds ;</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;        stats [Colamd::Info1] = col ;</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;        stats [Colamd::Info2] = row ;</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;        stats [Colamd::Info3] = n_row ;</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;        COLAMD_DEBUG0 ((<span class="stringliteral">&quot;colamd: row %d col %d out of bounds\n&quot;</span>, row, col)) ;</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;        <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;      }</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160; </div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;      <span class="keywordflow">if</span> (row &lt;= last_row || Row [row].shared2.mark == col)</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;      {</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;        <span class="comment">/* row index are unsorted or repeated (or both), thus col */</span></div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;        <span class="comment">/* is jumbled.  This is a notice, not an error condition. */</span></div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;        stats [Colamd::Status] = Colamd::OkButJumbled ;</div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;        stats [Colamd::Info1] = col ;</div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;        stats [Colamd::Info2] = row ;</div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;        (stats [Colamd::Info3]) ++ ;</div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;        COLAMD_DEBUG1 ((<span class="stringliteral">&quot;colamd: row %d col %d unsorted/duplicate\n&quot;</span>,row,col));</div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;      }</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160; </div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;      <span class="keywordflow">if</span> (Row [row].shared2.mark != col)</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;      {</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;        Row [row].length++ ;</div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;      }</div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;      <span class="keywordflow">else</span></div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;      {</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;        <span class="comment">/* this is a repeated entry in the column, */</span></div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;        <span class="comment">/* it will be removed */</span></div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;        Col [col].length-- ;</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;      }</div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160; </div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;      <span class="comment">/* mark the row as having been seen in this column */</span></div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;      Row [row].shared2.mark = col ;</div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160; </div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;      last_row = row ;</div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;    }</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;  }</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160; </div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;  <span class="comment">/* === Compute row pointers ============================================= */</span></div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160; </div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;  <span class="comment">/* row form of the matrix starts directly after the column */</span></div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;  <span class="comment">/* form of matrix in A */</span></div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;  Row [0].start = p [n_col] ;</div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;  Row [0].shared1.p = Row [0].start ;</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;  Row [0].shared2.mark = -1 ;</div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;  <span class="keywordflow">for</span> (row = 1 ; row &lt; n_row ; row++)</div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;  {</div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;    Row [row].start = Row [row-1].start + Row [row-1].length ;</div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;    Row [row].shared1.p = Row [row].start ;</div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;    Row [row].shared2.mark = -1 ;</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;  }</div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160; </div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;  <span class="comment">/* === Create row form ================================================== */</span></div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160; </div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;  <span class="keywordflow">if</span> (stats [Status] == OkButJumbled)</div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;  {</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;    <span class="comment">/* if cols jumbled, watch for repeated row indices */</span></div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;    <span class="keywordflow">for</span> (col = 0 ; col &lt; n_col ; col++)</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;    {</div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;      cp = &amp;A [p [col]] ;</div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160;      cp_end = &amp;A [p [col+1]] ;</div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;      <span class="keywordflow">while</span> (cp &lt; cp_end)</div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;      {</div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;        row = *cp++ ;</div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160;        <span class="keywordflow">if</span> (Row [row].shared2.mark != col)</div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;        {</div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160;          A [(Row [row].shared1.p)++] = col ;</div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;          Row [row].shared2.mark = col ;</div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;        }</div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160;      }</div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;    }</div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;  }</div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;  {</div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;    <span class="comment">/* if cols not jumbled, we don&#39;t need the mark (this is faster) */</span></div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;    <span class="keywordflow">for</span> (col = 0 ; col &lt; n_col ; col++)</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;    {</div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;      cp = &amp;A [p [col]] ;</div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;      cp_end = &amp;A [p [col+1]] ;</div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;      <span class="keywordflow">while</span> (cp &lt; cp_end)</div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160;      {</div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;        A [(Row [*cp++].shared1.p)++] = col ;</div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;      }</div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;    }</div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;  }</div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160; </div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;  <span class="comment">/* === Clear the row marks and set row degrees ========================== */</span></div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160; </div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160;  <span class="keywordflow">for</span> (row = 0 ; row &lt; n_row ; row++)</div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;  {</div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;    Row [row].shared2.mark = 0 ;</div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;    Row [row].shared1.degree = Row [row].length ;</div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160;  }</div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160; </div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;  <span class="comment">/* === See if we need to re-create columns ============================== */</span></div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160; </div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;  <span class="keywordflow">if</span> (stats [Status] == OkButJumbled)</div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;  {</div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;    COLAMD_DEBUG0 ((<span class="stringliteral">&quot;colamd: reconstructing column form, matrix jumbled\n&quot;</span>)) ;</div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160; </div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160; </div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;    <span class="comment">/* === Compute col pointers ========================================= */</span></div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160; </div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;    <span class="comment">/* col form of the matrix starts at A [0]. */</span></div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160;    <span class="comment">/* Note, we may have a gap between the col form and the row */</span></div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;    <span class="comment">/* form if there were duplicate entries, if so, it will be */</span></div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;    <span class="comment">/* removed upon the first garbage collection */</span></div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;    Col [0].start = 0 ;</div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;    p [0] = Col [0].start ;</div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;    <span class="keywordflow">for</span> (col = 1 ; col &lt; n_col ; col++)</div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160;    {</div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;      <span class="comment">/* note that the lengths here are for pruned columns, i.e. */</span></div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160;      <span class="comment">/* no duplicate row indices will exist for these columns */</span></div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160;      Col [col].start = Col [col-1].start + Col [col-1].length ;</div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160;      p [col] = Col [col].start ;</div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160;    }</div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160; </div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160;    <span class="comment">/* === Re-create col form =========================================== */</span></div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160; </div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160;    <span class="keywordflow">for</span> (row = 0 ; row &lt; n_row ; row++)</div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;    {</div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;      rp = &amp;A [Row [row].start] ;</div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160;      rp_end = rp + Row [row].length ;</div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160;      <span class="keywordflow">while</span> (rp &lt; rp_end)</div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160;      {</div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;        A [(p [*rp++])++] = row ;</div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160;      }</div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;    }</div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160;  }</div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160; </div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160;  <span class="comment">/* === Done.  Matrix is not (or no longer) jumbled ====================== */</span></div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160; </div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160;  <span class="keywordflow">return</span> (<span class="keyword">true</span>) ;</div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;}</div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160; </div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160; </div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160;<span class="comment">/* === init_scoring ========================================================= */</span></div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160; </div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160;<span class="comment">  Kills dense or empty columns and rows, calculates an initial score for</span></div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160;<span class="comment">  each column, and places all columns in the degree lists.  Not user-callable.</span></div>
<div class="line"><a name="l00715"></a><span class="lineno">  715</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00717"></a><span class="lineno">  717</span>&#160;<span class="keyword">static</span> <span class="keywordtype">void</span> init_scoring</div>
<div class="line"><a name="l00718"></a><span class="lineno">  718</span>&#160;  (</div>
<div class="line"><a name="l00719"></a><span class="lineno">  719</span>&#160;    <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l00720"></a><span class="lineno">  720</span>&#160; </div>
<div class="line"><a name="l00721"></a><span class="lineno">  721</span>&#160;    IndexType n_row,      <span class="comment">/* number of rows of A */</span></div>
<div class="line"><a name="l00722"></a><span class="lineno">  722</span>&#160;    IndexType n_col,      <span class="comment">/* number of columns of A */</span></div>
<div class="line"><a name="l00723"></a><span class="lineno">  723</span>&#160;    RowStructure&lt;IndexType&gt; Row [],    <span class="comment">/* of size n_row+1 */</span></div>
<div class="line"><a name="l00724"></a><span class="lineno">  724</span>&#160;    ColStructure&lt;IndexType&gt; Col [],    <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l00725"></a><span class="lineno">  725</span>&#160;    IndexType A [],     <span class="comment">/* column form and row form of A */</span></div>
<div class="line"><a name="l00726"></a><span class="lineno">  726</span>&#160;    IndexType head [],    <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l00727"></a><span class="lineno">  727</span>&#160;    <span class="keywordtype">double</span> knobs [NKnobs],<span class="comment">/* parameters */</span></div>
<div class="line"><a name="l00728"></a><span class="lineno">  728</span>&#160;    IndexType *p_n_row2,    <span class="comment">/* number of non-dense, non-empty rows */</span></div>
<div class="line"><a name="l00729"></a><span class="lineno">  729</span>&#160;    IndexType *p_n_col2,    <span class="comment">/* number of non-dense, non-empty columns */</span></div>
<div class="line"><a name="l00730"></a><span class="lineno">  730</span>&#160;    IndexType *p_max_deg    <span class="comment">/* maximum row degree */</span></div>
<div class="line"><a name="l00731"></a><span class="lineno">  731</span>&#160;    )</div>
<div class="line"><a name="l00732"></a><span class="lineno">  732</span>&#160;{</div>
<div class="line"><a name="l00733"></a><span class="lineno">  733</span>&#160;  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l00734"></a><span class="lineno">  734</span>&#160; </div>
<div class="line"><a name="l00735"></a><span class="lineno">  735</span>&#160;  IndexType c ;     <span class="comment">/* a column index */</span></div>
<div class="line"><a name="l00736"></a><span class="lineno">  736</span>&#160;  IndexType r, row ;    <span class="comment">/* a row index */</span></div>
<div class="line"><a name="l00737"></a><span class="lineno">  737</span>&#160;  IndexType *cp ;     <span class="comment">/* a column pointer */</span></div>
<div class="line"><a name="l00738"></a><span class="lineno">  738</span>&#160;  IndexType deg ;     <span class="comment">/* degree of a row or column */</span></div>
<div class="line"><a name="l00739"></a><span class="lineno">  739</span>&#160;  IndexType *cp_end ;   <span class="comment">/* a pointer to the end of a column */</span></div>
<div class="line"><a name="l00740"></a><span class="lineno">  740</span>&#160;  IndexType *new_cp ;   <span class="comment">/* new column pointer */</span></div>
<div class="line"><a name="l00741"></a><span class="lineno">  741</span>&#160;  IndexType col_length ;    <span class="comment">/* length of pruned column */</span></div>
<div class="line"><a name="l00742"></a><span class="lineno">  742</span>&#160;  IndexType score ;     <span class="comment">/* current column score */</span></div>
<div class="line"><a name="l00743"></a><span class="lineno">  743</span>&#160;  IndexType n_col2 ;    <span class="comment">/* number of non-dense, non-empty columns */</span></div>
<div class="line"><a name="l00744"></a><span class="lineno">  744</span>&#160;  IndexType n_row2 ;    <span class="comment">/* number of non-dense, non-empty rows */</span></div>
<div class="line"><a name="l00745"></a><span class="lineno">  745</span>&#160;  IndexType dense_row_count ; <span class="comment">/* remove rows with more entries than this */</span></div>
<div class="line"><a name="l00746"></a><span class="lineno">  746</span>&#160;  IndexType dense_col_count ; <span class="comment">/* remove cols with more entries than this */</span></div>
<div class="line"><a name="l00747"></a><span class="lineno">  747</span>&#160;  IndexType min_score ;   <span class="comment">/* smallest column score */</span></div>
<div class="line"><a name="l00748"></a><span class="lineno">  748</span>&#160;  IndexType max_deg ;   <span class="comment">/* maximum row degree */</span></div>
<div class="line"><a name="l00749"></a><span class="lineno">  749</span>&#160;  IndexType next_col ;    <span class="comment">/* Used to add to degree list.*/</span></div>
<div class="line"><a name="l00750"></a><span class="lineno">  750</span>&#160; </div>
<div class="line"><a name="l00751"></a><span class="lineno">  751</span>&#160; </div>
<div class="line"><a name="l00752"></a><span class="lineno">  752</span>&#160;  <span class="comment">/* === Extract knobs ==================================================== */</span></div>
<div class="line"><a name="l00753"></a><span class="lineno">  753</span>&#160; </div>
<div class="line"><a name="l00754"></a><span class="lineno">  754</span>&#160;  dense_row_count = numext::maxi(IndexType(0), numext::mini(IndexType(knobs [Colamd::DenseRow] * n_col), n_col)) ;</div>
<div class="line"><a name="l00755"></a><span class="lineno">  755</span>&#160;  dense_col_count = numext::maxi(IndexType(0), numext::mini(IndexType(knobs [Colamd::DenseCol] * n_row), n_row)) ;</div>
<div class="line"><a name="l00756"></a><span class="lineno">  756</span>&#160;  COLAMD_DEBUG1 ((<span class="stringliteral">&quot;colamd: densecount: %d %d\n&quot;</span>, dense_row_count, dense_col_count)) ;</div>
<div class="line"><a name="l00757"></a><span class="lineno">  757</span>&#160;  max_deg = 0 ;</div>
<div class="line"><a name="l00758"></a><span class="lineno">  758</span>&#160;  n_col2 = n_col ;</div>
<div class="line"><a name="l00759"></a><span class="lineno">  759</span>&#160;  n_row2 = n_row ;</div>
<div class="line"><a name="l00760"></a><span class="lineno">  760</span>&#160; </div>
<div class="line"><a name="l00761"></a><span class="lineno">  761</span>&#160;  <span class="comment">/* === Kill empty columns =============================================== */</span></div>
<div class="line"><a name="l00762"></a><span class="lineno">  762</span>&#160; </div>
<div class="line"><a name="l00763"></a><span class="lineno">  763</span>&#160;  <span class="comment">/* Put the empty columns at the end in their natural order, so that LU */</span></div>
<div class="line"><a name="l00764"></a><span class="lineno">  764</span>&#160;  <span class="comment">/* factorization can proceed as far as possible. */</span></div>
<div class="line"><a name="l00765"></a><span class="lineno">  765</span>&#160;  <span class="keywordflow">for</span> (c = n_col-1 ; c &gt;= 0 ; c--)</div>
<div class="line"><a name="l00766"></a><span class="lineno">  766</span>&#160;  {</div>
<div class="line"><a name="l00767"></a><span class="lineno">  767</span>&#160;    deg = Col [c].length ;</div>
<div class="line"><a name="l00768"></a><span class="lineno">  768</span>&#160;    <span class="keywordflow">if</span> (deg == 0)</div>
<div class="line"><a name="l00769"></a><span class="lineno">  769</span>&#160;    {</div>
<div class="line"><a name="l00770"></a><span class="lineno">  770</span>&#160;      <span class="comment">/* this is a empty column, kill and order it last */</span></div>
<div class="line"><a name="l00771"></a><span class="lineno">  771</span>&#160;      Col [c].shared2.order = --n_col2 ;</div>
<div class="line"><a name="l00772"></a><span class="lineno">  772</span>&#160;      Col[c].kill_principal() ;</div>
<div class="line"><a name="l00773"></a><span class="lineno">  773</span>&#160;    }</div>
<div class="line"><a name="l00774"></a><span class="lineno">  774</span>&#160;  }</div>
<div class="line"><a name="l00775"></a><span class="lineno">  775</span>&#160;  COLAMD_DEBUG1 ((<span class="stringliteral">&quot;colamd: null columns killed: %d\n&quot;</span>, n_col - n_col2)) ;</div>
<div class="line"><a name="l00776"></a><span class="lineno">  776</span>&#160; </div>
<div class="line"><a name="l00777"></a><span class="lineno">  777</span>&#160;  <span class="comment">/* === Kill dense columns =============================================== */</span></div>
<div class="line"><a name="l00778"></a><span class="lineno">  778</span>&#160; </div>
<div class="line"><a name="l00779"></a><span class="lineno">  779</span>&#160;  <span class="comment">/* Put the dense columns at the end, in their natural order */</span></div>
<div class="line"><a name="l00780"></a><span class="lineno">  780</span>&#160;  <span class="keywordflow">for</span> (c = n_col-1 ; c &gt;= 0 ; c--)</div>
<div class="line"><a name="l00781"></a><span class="lineno">  781</span>&#160;  {</div>
<div class="line"><a name="l00782"></a><span class="lineno">  782</span>&#160;    <span class="comment">/* skip any dead columns */</span></div>
<div class="line"><a name="l00783"></a><span class="lineno">  783</span>&#160;    <span class="keywordflow">if</span> (Col[c].is_dead())</div>
<div class="line"><a name="l00784"></a><span class="lineno">  784</span>&#160;    {</div>
<div class="line"><a name="l00785"></a><span class="lineno">  785</span>&#160;      continue ;</div>
<div class="line"><a name="l00786"></a><span class="lineno">  786</span>&#160;    }</div>
<div class="line"><a name="l00787"></a><span class="lineno">  787</span>&#160;    deg = Col [c].length ;</div>
<div class="line"><a name="l00788"></a><span class="lineno">  788</span>&#160;    <span class="keywordflow">if</span> (deg &gt; dense_col_count)</div>
<div class="line"><a name="l00789"></a><span class="lineno">  789</span>&#160;    {</div>
<div class="line"><a name="l00790"></a><span class="lineno">  790</span>&#160;      <span class="comment">/* this is a dense column, kill and order it last */</span></div>
<div class="line"><a name="l00791"></a><span class="lineno">  791</span>&#160;      Col [c].shared2.order = --n_col2 ;</div>
<div class="line"><a name="l00792"></a><span class="lineno">  792</span>&#160;      <span class="comment">/* decrement the row degrees */</span></div>
<div class="line"><a name="l00793"></a><span class="lineno">  793</span>&#160;      cp = &amp;A [Col [c].start] ;</div>
<div class="line"><a name="l00794"></a><span class="lineno">  794</span>&#160;      cp_end = cp + Col [c].length ;</div>
<div class="line"><a name="l00795"></a><span class="lineno">  795</span>&#160;      <span class="keywordflow">while</span> (cp &lt; cp_end)</div>
<div class="line"><a name="l00796"></a><span class="lineno">  796</span>&#160;      {</div>
<div class="line"><a name="l00797"></a><span class="lineno">  797</span>&#160;        Row [*cp++].shared1.degree-- ;</div>
<div class="line"><a name="l00798"></a><span class="lineno">  798</span>&#160;      }</div>
<div class="line"><a name="l00799"></a><span class="lineno">  799</span>&#160;      Col[c].kill_principal() ;</div>
<div class="line"><a name="l00800"></a><span class="lineno">  800</span>&#160;    }</div>
<div class="line"><a name="l00801"></a><span class="lineno">  801</span>&#160;  }</div>
<div class="line"><a name="l00802"></a><span class="lineno">  802</span>&#160;  COLAMD_DEBUG1 ((<span class="stringliteral">&quot;colamd: Dense and null columns killed: %d\n&quot;</span>, n_col - n_col2)) ;</div>
<div class="line"><a name="l00803"></a><span class="lineno">  803</span>&#160; </div>
<div class="line"><a name="l00804"></a><span class="lineno">  804</span>&#160;  <span class="comment">/* === Kill dense and empty rows ======================================== */</span></div>
<div class="line"><a name="l00805"></a><span class="lineno">  805</span>&#160; </div>
<div class="line"><a name="l00806"></a><span class="lineno">  806</span>&#160;  <span class="keywordflow">for</span> (r = 0 ; r &lt; n_row ; r++)</div>
<div class="line"><a name="l00807"></a><span class="lineno">  807</span>&#160;  {</div>
<div class="line"><a name="l00808"></a><span class="lineno">  808</span>&#160;    deg = Row [r].shared1.degree ;</div>
<div class="line"><a name="l00809"></a><span class="lineno">  809</span>&#160;    COLAMD_ASSERT (deg &gt;= 0 &amp;&amp; deg &lt;= n_col) ;</div>
<div class="line"><a name="l00810"></a><span class="lineno">  810</span>&#160;    <span class="keywordflow">if</span> (deg &gt; dense_row_count || deg == 0)</div>
<div class="line"><a name="l00811"></a><span class="lineno">  811</span>&#160;    {</div>
<div class="line"><a name="l00812"></a><span class="lineno">  812</span>&#160;      <span class="comment">/* kill a dense or empty row */</span></div>
<div class="line"><a name="l00813"></a><span class="lineno">  813</span>&#160;      Row[r].kill() ;</div>
<div class="line"><a name="l00814"></a><span class="lineno">  814</span>&#160;      --n_row2 ;</div>
<div class="line"><a name="l00815"></a><span class="lineno">  815</span>&#160;    }</div>
<div class="line"><a name="l00816"></a><span class="lineno">  816</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00817"></a><span class="lineno">  817</span>&#160;    {</div>
<div class="line"><a name="l00818"></a><span class="lineno">  818</span>&#160;      <span class="comment">/* keep track of max degree of remaining rows */</span></div>
<div class="line"><a name="l00819"></a><span class="lineno">  819</span>&#160;      max_deg = numext::maxi(max_deg, deg) ;</div>
<div class="line"><a name="l00820"></a><span class="lineno">  820</span>&#160;    }</div>
<div class="line"><a name="l00821"></a><span class="lineno">  821</span>&#160;  }</div>
<div class="line"><a name="l00822"></a><span class="lineno">  822</span>&#160;  COLAMD_DEBUG1 ((<span class="stringliteral">&quot;colamd: Dense and null rows killed: %d\n&quot;</span>, n_row - n_row2)) ;</div>
<div class="line"><a name="l00823"></a><span class="lineno">  823</span>&#160; </div>
<div class="line"><a name="l00824"></a><span class="lineno">  824</span>&#160;  <span class="comment">/* === Compute initial column scores ==================================== */</span></div>
<div class="line"><a name="l00825"></a><span class="lineno">  825</span>&#160; </div>
<div class="line"><a name="l00826"></a><span class="lineno">  826</span>&#160;  <span class="comment">/* At this point the row degrees are accurate.  They reflect the number */</span></div>
<div class="line"><a name="l00827"></a><span class="lineno">  827</span>&#160;  <span class="comment">/* of &quot;live&quot; (non-dense) columns in each row.  No empty rows exist. */</span></div>
<div class="line"><a name="l00828"></a><span class="lineno">  828</span>&#160;  <span class="comment">/* Some &quot;live&quot; columns may contain only dead rows, however.  These are */</span></div>
<div class="line"><a name="l00829"></a><span class="lineno">  829</span>&#160;  <span class="comment">/* pruned in the code below. */</span></div>
<div class="line"><a name="l00830"></a><span class="lineno">  830</span>&#160; </div>
<div class="line"><a name="l00831"></a><span class="lineno">  831</span>&#160;  <span class="comment">/* now find the initial matlab score for each column */</span></div>
<div class="line"><a name="l00832"></a><span class="lineno">  832</span>&#160;  <span class="keywordflow">for</span> (c = n_col-1 ; c &gt;= 0 ; c--)</div>
<div class="line"><a name="l00833"></a><span class="lineno">  833</span>&#160;  {</div>
<div class="line"><a name="l00834"></a><span class="lineno">  834</span>&#160;    <span class="comment">/* skip dead column */</span></div>
<div class="line"><a name="l00835"></a><span class="lineno">  835</span>&#160;    <span class="keywordflow">if</span> (Col[c].is_dead())</div>
<div class="line"><a name="l00836"></a><span class="lineno">  836</span>&#160;    {</div>
<div class="line"><a name="l00837"></a><span class="lineno">  837</span>&#160;      continue ;</div>
<div class="line"><a name="l00838"></a><span class="lineno">  838</span>&#160;    }</div>
<div class="line"><a name="l00839"></a><span class="lineno">  839</span>&#160;    score = 0 ;</div>
<div class="line"><a name="l00840"></a><span class="lineno">  840</span>&#160;    cp = &amp;A [Col [c].start] ;</div>
<div class="line"><a name="l00841"></a><span class="lineno">  841</span>&#160;    new_cp = cp ;</div>
<div class="line"><a name="l00842"></a><span class="lineno">  842</span>&#160;    cp_end = cp + Col [c].length ;</div>
<div class="line"><a name="l00843"></a><span class="lineno">  843</span>&#160;    <span class="keywordflow">while</span> (cp &lt; cp_end)</div>
<div class="line"><a name="l00844"></a><span class="lineno">  844</span>&#160;    {</div>
<div class="line"><a name="l00845"></a><span class="lineno">  845</span>&#160;      <span class="comment">/* get a row */</span></div>
<div class="line"><a name="l00846"></a><span class="lineno">  846</span>&#160;      row = *cp++ ;</div>
<div class="line"><a name="l00847"></a><span class="lineno">  847</span>&#160;      <span class="comment">/* skip if dead */</span></div>
<div class="line"><a name="l00848"></a><span class="lineno">  848</span>&#160;      <span class="keywordflow">if</span> (Row[row].is_dead())</div>
<div class="line"><a name="l00849"></a><span class="lineno">  849</span>&#160;      {</div>
<div class="line"><a name="l00850"></a><span class="lineno">  850</span>&#160;        continue ;</div>
<div class="line"><a name="l00851"></a><span class="lineno">  851</span>&#160;      }</div>
<div class="line"><a name="l00852"></a><span class="lineno">  852</span>&#160;      <span class="comment">/* compact the column */</span></div>
<div class="line"><a name="l00853"></a><span class="lineno">  853</span>&#160;      *new_cp++ = row ;</div>
<div class="line"><a name="l00854"></a><span class="lineno">  854</span>&#160;      <span class="comment">/* add row&#39;s external degree */</span></div>
<div class="line"><a name="l00855"></a><span class="lineno">  855</span>&#160;      score += Row [row].shared1.degree - 1 ;</div>
<div class="line"><a name="l00856"></a><span class="lineno">  856</span>&#160;      <span class="comment">/* guard against integer overflow */</span></div>
<div class="line"><a name="l00857"></a><span class="lineno">  857</span>&#160;      score = numext::mini(score, n_col) ;</div>
<div class="line"><a name="l00858"></a><span class="lineno">  858</span>&#160;    }</div>
<div class="line"><a name="l00859"></a><span class="lineno">  859</span>&#160;    <span class="comment">/* determine pruned column length */</span></div>
<div class="line"><a name="l00860"></a><span class="lineno">  860</span>&#160;    col_length = (IndexType) (new_cp - &amp;A [Col [c].start]) ;</div>
<div class="line"><a name="l00861"></a><span class="lineno">  861</span>&#160;    <span class="keywordflow">if</span> (col_length == 0)</div>
<div class="line"><a name="l00862"></a><span class="lineno">  862</span>&#160;    {</div>
<div class="line"><a name="l00863"></a><span class="lineno">  863</span>&#160;      <span class="comment">/* a newly-made null column (all rows in this col are &quot;dense&quot; */</span></div>
<div class="line"><a name="l00864"></a><span class="lineno">  864</span>&#160;      <span class="comment">/* and have already been killed) */</span></div>
<div class="line"><a name="l00865"></a><span class="lineno">  865</span>&#160;      COLAMD_DEBUG2 ((<span class="stringliteral">&quot;Newly null killed: %d\n&quot;</span>, c)) ;</div>
<div class="line"><a name="l00866"></a><span class="lineno">  866</span>&#160;      Col [c].shared2.order = --n_col2 ;</div>
<div class="line"><a name="l00867"></a><span class="lineno">  867</span>&#160;      Col[c].kill_principal() ;</div>
<div class="line"><a name="l00868"></a><span class="lineno">  868</span>&#160;    }</div>
<div class="line"><a name="l00869"></a><span class="lineno">  869</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00870"></a><span class="lineno">  870</span>&#160;    {</div>
<div class="line"><a name="l00871"></a><span class="lineno">  871</span>&#160;      <span class="comment">/* set column length and set score */</span></div>
<div class="line"><a name="l00872"></a><span class="lineno">  872</span>&#160;      COLAMD_ASSERT (score &gt;= 0) ;</div>
<div class="line"><a name="l00873"></a><span class="lineno">  873</span>&#160;      COLAMD_ASSERT (score &lt;= n_col) ;</div>
<div class="line"><a name="l00874"></a><span class="lineno">  874</span>&#160;      Col [c].length = col_length ;</div>
<div class="line"><a name="l00875"></a><span class="lineno">  875</span>&#160;      Col [c].shared2.score = score ;</div>
<div class="line"><a name="l00876"></a><span class="lineno">  876</span>&#160;    }</div>
<div class="line"><a name="l00877"></a><span class="lineno">  877</span>&#160;  }</div>
<div class="line"><a name="l00878"></a><span class="lineno">  878</span>&#160;  COLAMD_DEBUG1 ((<span class="stringliteral">&quot;colamd: Dense, null, and newly-null columns killed: %d\n&quot;</span>,</div>
<div class="line"><a name="l00879"></a><span class="lineno">  879</span>&#160;                  n_col-n_col2)) ;</div>
<div class="line"><a name="l00880"></a><span class="lineno">  880</span>&#160; </div>
<div class="line"><a name="l00881"></a><span class="lineno">  881</span>&#160;  <span class="comment">/* At this point, all empty rows and columns are dead.  All live columns */</span></div>
<div class="line"><a name="l00882"></a><span class="lineno">  882</span>&#160;  <span class="comment">/* are &quot;clean&quot; (containing no dead rows) and simplicial (no supercolumns */</span></div>
<div class="line"><a name="l00883"></a><span class="lineno">  883</span>&#160;  <span class="comment">/* yet).  Rows may contain dead columns, but all live rows contain at */</span></div>
<div class="line"><a name="l00884"></a><span class="lineno">  884</span>&#160;  <span class="comment">/* least one live column. */</span></div>
<div class="line"><a name="l00885"></a><span class="lineno">  885</span>&#160; </div>
<div class="line"><a name="l00886"></a><span class="lineno">  886</span>&#160;  <span class="comment">/* === Initialize degree lists ========================================== */</span></div>
<div class="line"><a name="l00887"></a><span class="lineno">  887</span>&#160; </div>
<div class="line"><a name="l00888"></a><span class="lineno">  888</span>&#160; </div>
<div class="line"><a name="l00889"></a><span class="lineno">  889</span>&#160;  <span class="comment">/* clear the hash buckets */</span></div>
<div class="line"><a name="l00890"></a><span class="lineno">  890</span>&#160;  <span class="keywordflow">for</span> (c = 0 ; c &lt;= n_col ; c++)</div>
<div class="line"><a name="l00891"></a><span class="lineno">  891</span>&#160;  {</div>
<div class="line"><a name="l00892"></a><span class="lineno">  892</span>&#160;    head [c] = Empty ;</div>
<div class="line"><a name="l00893"></a><span class="lineno">  893</span>&#160;  }</div>
<div class="line"><a name="l00894"></a><span class="lineno">  894</span>&#160;  min_score = n_col ;</div>
<div class="line"><a name="l00895"></a><span class="lineno">  895</span>&#160;  <span class="comment">/* place in reverse order, so low column indices are at the front */</span></div>
<div class="line"><a name="l00896"></a><span class="lineno">  896</span>&#160;  <span class="comment">/* of the lists.  This is to encourage natural tie-breaking */</span></div>
<div class="line"><a name="l00897"></a><span class="lineno">  897</span>&#160;  <span class="keywordflow">for</span> (c = n_col-1 ; c &gt;= 0 ; c--)</div>
<div class="line"><a name="l00898"></a><span class="lineno">  898</span>&#160;  {</div>
<div class="line"><a name="l00899"></a><span class="lineno">  899</span>&#160;    <span class="comment">/* only add principal columns to degree lists */</span></div>
<div class="line"><a name="l00900"></a><span class="lineno">  900</span>&#160;    <span class="keywordflow">if</span> (Col[c].is_alive())</div>
<div class="line"><a name="l00901"></a><span class="lineno">  901</span>&#160;    {</div>
<div class="line"><a name="l00902"></a><span class="lineno">  902</span>&#160;      COLAMD_DEBUG4 ((<span class="stringliteral">&quot;place %d score %d minscore %d ncol %d\n&quot;</span>,</div>
<div class="line"><a name="l00903"></a><span class="lineno">  903</span>&#160;                      c, Col [c].shared2.score, min_score, n_col)) ;</div>
<div class="line"><a name="l00904"></a><span class="lineno">  904</span>&#160; </div>
<div class="line"><a name="l00905"></a><span class="lineno">  905</span>&#160;      <span class="comment">/* === Add columns score to DList =============================== */</span></div>
<div class="line"><a name="l00906"></a><span class="lineno">  906</span>&#160; </div>
<div class="line"><a name="l00907"></a><span class="lineno">  907</span>&#160;      score = Col [c].shared2.score ;</div>
<div class="line"><a name="l00908"></a><span class="lineno">  908</span>&#160; </div>
<div class="line"><a name="l00909"></a><span class="lineno">  909</span>&#160;      COLAMD_ASSERT (min_score &gt;= 0) ;</div>
<div class="line"><a name="l00910"></a><span class="lineno">  910</span>&#160;      COLAMD_ASSERT (min_score &lt;= n_col) ;</div>
<div class="line"><a name="l00911"></a><span class="lineno">  911</span>&#160;      COLAMD_ASSERT (score &gt;= 0) ;</div>
<div class="line"><a name="l00912"></a><span class="lineno">  912</span>&#160;      COLAMD_ASSERT (score &lt;= n_col) ;</div>
<div class="line"><a name="l00913"></a><span class="lineno">  913</span>&#160;      COLAMD_ASSERT (head [score] &gt;= Empty) ;</div>
<div class="line"><a name="l00914"></a><span class="lineno">  914</span>&#160; </div>
<div class="line"><a name="l00915"></a><span class="lineno">  915</span>&#160;      <span class="comment">/* now add this column to dList at proper score location */</span></div>
<div class="line"><a name="l00916"></a><span class="lineno">  916</span>&#160;      next_col = head [score] ;</div>
<div class="line"><a name="l00917"></a><span class="lineno">  917</span>&#160;      Col [c].shared3.prev = Empty ;</div>
<div class="line"><a name="l00918"></a><span class="lineno">  918</span>&#160;      Col [c].shared4.degree_next = next_col ;</div>
<div class="line"><a name="l00919"></a><span class="lineno">  919</span>&#160; </div>
<div class="line"><a name="l00920"></a><span class="lineno">  920</span>&#160;      <span class="comment">/* if there already was a column with the same score, set its */</span></div>
<div class="line"><a name="l00921"></a><span class="lineno">  921</span>&#160;      <span class="comment">/* previous pointer to this new column */</span></div>
<div class="line"><a name="l00922"></a><span class="lineno">  922</span>&#160;      <span class="keywordflow">if</span> (next_col != Empty)</div>
<div class="line"><a name="l00923"></a><span class="lineno">  923</span>&#160;      {</div>
<div class="line"><a name="l00924"></a><span class="lineno">  924</span>&#160;        Col [next_col].shared3.prev = c ;</div>
<div class="line"><a name="l00925"></a><span class="lineno">  925</span>&#160;      }</div>
<div class="line"><a name="l00926"></a><span class="lineno">  926</span>&#160;      head [score] = c ;</div>
<div class="line"><a name="l00927"></a><span class="lineno">  927</span>&#160; </div>
<div class="line"><a name="l00928"></a><span class="lineno">  928</span>&#160;      <span class="comment">/* see if this score is less than current min */</span></div>
<div class="line"><a name="l00929"></a><span class="lineno">  929</span>&#160;      min_score = numext::mini(min_score, score) ;</div>
<div class="line"><a name="l00930"></a><span class="lineno">  930</span>&#160; </div>
<div class="line"><a name="l00931"></a><span class="lineno">  931</span>&#160; </div>
<div class="line"><a name="l00932"></a><span class="lineno">  932</span>&#160;    }</div>
<div class="line"><a name="l00933"></a><span class="lineno">  933</span>&#160;  }</div>
<div class="line"><a name="l00934"></a><span class="lineno">  934</span>&#160; </div>
<div class="line"><a name="l00935"></a><span class="lineno">  935</span>&#160; </div>
<div class="line"><a name="l00936"></a><span class="lineno">  936</span>&#160;  <span class="comment">/* === Return number of remaining columns, and max row degree =========== */</span></div>
<div class="line"><a name="l00937"></a><span class="lineno">  937</span>&#160; </div>
<div class="line"><a name="l00938"></a><span class="lineno">  938</span>&#160;  *p_n_col2 = n_col2 ;</div>
<div class="line"><a name="l00939"></a><span class="lineno">  939</span>&#160;  *p_n_row2 = n_row2 ;</div>
<div class="line"><a name="l00940"></a><span class="lineno">  940</span>&#160;  *p_max_deg = max_deg ;</div>
<div class="line"><a name="l00941"></a><span class="lineno">  941</span>&#160;}</div>
<div class="line"><a name="l00942"></a><span class="lineno">  942</span>&#160; </div>
<div class="line"><a name="l00943"></a><span class="lineno">  943</span>&#160; </div>
<div class="line"><a name="l00944"></a><span class="lineno">  944</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00945"></a><span class="lineno">  945</span>&#160;<span class="comment">/* === find_ordering ======================================================== */</span></div>
<div class="line"><a name="l00946"></a><span class="lineno">  946</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00947"></a><span class="lineno">  947</span>&#160; </div>
<div class="line"><a name="l00948"></a><span class="lineno">  948</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00949"></a><span class="lineno">  949</span>&#160;<span class="comment">  Order the principal columns of the supercolumn form of the matrix</span></div>
<div class="line"><a name="l00950"></a><span class="lineno">  950</span>&#160;<span class="comment">  (no supercolumns on input).  Uses a minimum approximate column minimum</span></div>
<div class="line"><a name="l00951"></a><span class="lineno">  951</span>&#160;<span class="comment">  degree ordering method.  Not user-callable.</span></div>
<div class="line"><a name="l00952"></a><span class="lineno">  952</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00953"></a><span class="lineno">  953</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l00954"></a><span class="lineno">  954</span>&#160;<span class="keyword">static</span> IndexType find_ordering <span class="comment">/* return the number of garbage collections */</span></div>
<div class="line"><a name="l00955"></a><span class="lineno">  955</span>&#160;  (</div>
<div class="line"><a name="l00956"></a><span class="lineno">  956</span>&#160;    <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l00957"></a><span class="lineno">  957</span>&#160; </div>
<div class="line"><a name="l00958"></a><span class="lineno">  958</span>&#160;    IndexType n_row,      <span class="comment">/* number of rows of A */</span></div>
<div class="line"><a name="l00959"></a><span class="lineno">  959</span>&#160;    IndexType n_col,      <span class="comment">/* number of columns of A */</span></div>
<div class="line"><a name="l00960"></a><span class="lineno">  960</span>&#160;    IndexType Alen,     <span class="comment">/* size of A, 2*nnz + n_col or larger */</span></div>
<div class="line"><a name="l00961"></a><span class="lineno">  961</span>&#160;    RowStructure&lt;IndexType&gt; Row [],    <span class="comment">/* of size n_row+1 */</span></div>
<div class="line"><a name="l00962"></a><span class="lineno">  962</span>&#160;    ColStructure&lt;IndexType&gt; Col [],    <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l00963"></a><span class="lineno">  963</span>&#160;    IndexType A [],     <span class="comment">/* column form and row form of A */</span></div>
<div class="line"><a name="l00964"></a><span class="lineno">  964</span>&#160;    IndexType head [],    <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l00965"></a><span class="lineno">  965</span>&#160;    IndexType n_col2,     <span class="comment">/* Remaining columns to order */</span></div>
<div class="line"><a name="l00966"></a><span class="lineno">  966</span>&#160;    IndexType max_deg,    <span class="comment">/* Maximum row degree */</span></div>
<div class="line"><a name="l00967"></a><span class="lineno">  967</span>&#160;    IndexType pfree     <span class="comment">/* index of first free slot (2*nnz on entry) */</span></div>
<div class="line"><a name="l00968"></a><span class="lineno">  968</span>&#160;    )</div>
<div class="line"><a name="l00969"></a><span class="lineno">  969</span>&#160;{</div>
<div class="line"><a name="l00970"></a><span class="lineno">  970</span>&#160;  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l00971"></a><span class="lineno">  971</span>&#160; </div>
<div class="line"><a name="l00972"></a><span class="lineno">  972</span>&#160;  IndexType k ;     <span class="comment">/* current pivot ordering step */</span></div>
<div class="line"><a name="l00973"></a><span class="lineno">  973</span>&#160;  IndexType pivot_col ;   <span class="comment">/* current pivot column */</span></div>
<div class="line"><a name="l00974"></a><span class="lineno">  974</span>&#160;  IndexType *cp ;     <span class="comment">/* a column pointer */</span></div>
<div class="line"><a name="l00975"></a><span class="lineno">  975</span>&#160;  IndexType *rp ;     <span class="comment">/* a row pointer */</span></div>
<div class="line"><a name="l00976"></a><span class="lineno">  976</span>&#160;  IndexType pivot_row ;   <span class="comment">/* current pivot row */</span></div>
<div class="line"><a name="l00977"></a><span class="lineno">  977</span>&#160;  IndexType *new_cp ;   <span class="comment">/* modified column pointer */</span></div>
<div class="line"><a name="l00978"></a><span class="lineno">  978</span>&#160;  IndexType *new_rp ;   <span class="comment">/* modified row pointer */</span></div>
<div class="line"><a name="l00979"></a><span class="lineno">  979</span>&#160;  IndexType pivot_row_start ; <span class="comment">/* pointer to start of pivot row */</span></div>
<div class="line"><a name="l00980"></a><span class="lineno">  980</span>&#160;  IndexType pivot_row_degree ;  <span class="comment">/* number of columns in pivot row */</span></div>
<div class="line"><a name="l00981"></a><span class="lineno">  981</span>&#160;  IndexType pivot_row_length ;  <span class="comment">/* number of supercolumns in pivot row */</span></div>
<div class="line"><a name="l00982"></a><span class="lineno">  982</span>&#160;  IndexType pivot_col_score ; <span class="comment">/* score of pivot column */</span></div>
<div class="line"><a name="l00983"></a><span class="lineno">  983</span>&#160;  IndexType needed_memory ;   <span class="comment">/* free space needed for pivot row */</span></div>
<div class="line"><a name="l00984"></a><span class="lineno">  984</span>&#160;  IndexType *cp_end ;   <span class="comment">/* pointer to the end of a column */</span></div>
<div class="line"><a name="l00985"></a><span class="lineno">  985</span>&#160;  IndexType *rp_end ;   <span class="comment">/* pointer to the end of a row */</span></div>
<div class="line"><a name="l00986"></a><span class="lineno">  986</span>&#160;  IndexType row ;     <span class="comment">/* a row index */</span></div>
<div class="line"><a name="l00987"></a><span class="lineno">  987</span>&#160;  IndexType col ;     <span class="comment">/* a column index */</span></div>
<div class="line"><a name="l00988"></a><span class="lineno">  988</span>&#160;  IndexType max_score ;   <span class="comment">/* maximum possible score */</span></div>
<div class="line"><a name="l00989"></a><span class="lineno">  989</span>&#160;  IndexType cur_score ;   <span class="comment">/* score of current column */</span></div>
<div class="line"><a name="l00990"></a><span class="lineno">  990</span>&#160;  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> hash ;   <span class="comment">/* hash value for supernode detection */</span></div>
<div class="line"><a name="l00991"></a><span class="lineno">  991</span>&#160;  IndexType head_column ;   <span class="comment">/* head of hash bucket */</span></div>
<div class="line"><a name="l00992"></a><span class="lineno">  992</span>&#160;  IndexType first_col ;   <span class="comment">/* first column in hash bucket */</span></div>
<div class="line"><a name="l00993"></a><span class="lineno">  993</span>&#160;  IndexType tag_mark ;    <span class="comment">/* marker value for mark array */</span></div>
<div class="line"><a name="l00994"></a><span class="lineno">  994</span>&#160;  IndexType row_mark ;    <span class="comment">/* Row [row].shared2.mark */</span></div>
<div class="line"><a name="l00995"></a><span class="lineno">  995</span>&#160;  IndexType set_difference ;  <span class="comment">/* set difference size of row with pivot row */</span></div>
<div class="line"><a name="l00996"></a><span class="lineno">  996</span>&#160;  IndexType min_score ;   <span class="comment">/* smallest column score */</span></div>
<div class="line"><a name="l00997"></a><span class="lineno">  997</span>&#160;  IndexType col_thickness ;   <span class="comment">/* &quot;thickness&quot; (no. of columns in a supercol) */</span></div>
<div class="line"><a name="l00998"></a><span class="lineno">  998</span>&#160;  IndexType max_mark ;    <span class="comment">/* maximum value of tag_mark */</span></div>
<div class="line"><a name="l00999"></a><span class="lineno">  999</span>&#160;  IndexType pivot_col_thickness ; <span class="comment">/* number of columns represented by pivot col */</span></div>
<div class="line"><a name="l01000"></a><span class="lineno"> 1000</span>&#160;  IndexType prev_col ;    <span class="comment">/* Used by Dlist operations. */</span></div>
<div class="line"><a name="l01001"></a><span class="lineno"> 1001</span>&#160;  IndexType next_col ;    <span class="comment">/* Used by Dlist operations. */</span></div>
<div class="line"><a name="l01002"></a><span class="lineno"> 1002</span>&#160;  IndexType ngarbage ;    <span class="comment">/* number of garbage collections performed */</span></div>
<div class="line"><a name="l01003"></a><span class="lineno"> 1003</span>&#160; </div>
<div class="line"><a name="l01004"></a><span class="lineno"> 1004</span>&#160; </div>
<div class="line"><a name="l01005"></a><span class="lineno"> 1005</span>&#160;  <span class="comment">/* === Initialization and clear mark ==================================== */</span></div>
<div class="line"><a name="l01006"></a><span class="lineno"> 1006</span>&#160; </div>
<div class="line"><a name="l01007"></a><span class="lineno"> 1007</span>&#160;  max_mark = INT_MAX - n_col ;  <span class="comment">/* INT_MAX defined in &lt;limits.h&gt; */</span></div>
<div class="line"><a name="l01008"></a><span class="lineno"> 1008</span>&#160;  tag_mark = Colamd::clear_mark (n_row, Row) ;</div>
<div class="line"><a name="l01009"></a><span class="lineno"> 1009</span>&#160;  min_score = 0 ;</div>
<div class="line"><a name="l01010"></a><span class="lineno"> 1010</span>&#160;  ngarbage = 0 ;</div>
<div class="line"><a name="l01011"></a><span class="lineno"> 1011</span>&#160;  COLAMD_DEBUG1 ((<span class="stringliteral">&quot;colamd: Ordering, n_col2=%d\n&quot;</span>, n_col2)) ;</div>
<div class="line"><a name="l01012"></a><span class="lineno"> 1012</span>&#160; </div>
<div class="line"><a name="l01013"></a><span class="lineno"> 1013</span>&#160;  <span class="comment">/* === Order the columns ================================================ */</span></div>
<div class="line"><a name="l01014"></a><span class="lineno"> 1014</span>&#160; </div>
<div class="line"><a name="l01015"></a><span class="lineno"> 1015</span>&#160;  <span class="keywordflow">for</span> (k = 0 ; k &lt; n_col2 ; <span class="comment">/* &#39;k&#39; is incremented below */</span>)</div>
<div class="line"><a name="l01016"></a><span class="lineno"> 1016</span>&#160;  {</div>
<div class="line"><a name="l01017"></a><span class="lineno"> 1017</span>&#160; </div>
<div class="line"><a name="l01018"></a><span class="lineno"> 1018</span>&#160;    <span class="comment">/* === Select pivot column, and order it ============================ */</span></div>
<div class="line"><a name="l01019"></a><span class="lineno"> 1019</span>&#160; </div>
<div class="line"><a name="l01020"></a><span class="lineno"> 1020</span>&#160;    <span class="comment">/* make sure degree list isn&#39;t empty */</span></div>
<div class="line"><a name="l01021"></a><span class="lineno"> 1021</span>&#160;    COLAMD_ASSERT (min_score &gt;= 0) ;</div>
<div class="line"><a name="l01022"></a><span class="lineno"> 1022</span>&#160;    COLAMD_ASSERT (min_score &lt;= n_col) ;</div>
<div class="line"><a name="l01023"></a><span class="lineno"> 1023</span>&#160;    COLAMD_ASSERT (head [min_score] &gt;= Empty) ;</div>
<div class="line"><a name="l01024"></a><span class="lineno"> 1024</span>&#160; </div>
<div class="line"><a name="l01025"></a><span class="lineno"> 1025</span>&#160;    <span class="comment">/* get pivot column from head of minimum degree list */</span></div>
<div class="line"><a name="l01026"></a><span class="lineno"> 1026</span>&#160;    <span class="keywordflow">while</span> (min_score &lt; n_col &amp;&amp; head [min_score] == Empty)</div>
<div class="line"><a name="l01027"></a><span class="lineno"> 1027</span>&#160;    {</div>
<div class="line"><a name="l01028"></a><span class="lineno"> 1028</span>&#160;      min_score++ ;</div>
<div class="line"><a name="l01029"></a><span class="lineno"> 1029</span>&#160;    }</div>
<div class="line"><a name="l01030"></a><span class="lineno"> 1030</span>&#160;    pivot_col = head [min_score] ;</div>
<div class="line"><a name="l01031"></a><span class="lineno"> 1031</span>&#160;    COLAMD_ASSERT (pivot_col &gt;= 0 &amp;&amp; pivot_col &lt;= n_col) ;</div>
<div class="line"><a name="l01032"></a><span class="lineno"> 1032</span>&#160;    next_col = Col [pivot_col].shared4.degree_next ;</div>
<div class="line"><a name="l01033"></a><span class="lineno"> 1033</span>&#160;    head [min_score] = next_col ;</div>
<div class="line"><a name="l01034"></a><span class="lineno"> 1034</span>&#160;    <span class="keywordflow">if</span> (next_col != Empty)</div>
<div class="line"><a name="l01035"></a><span class="lineno"> 1035</span>&#160;    {</div>
<div class="line"><a name="l01036"></a><span class="lineno"> 1036</span>&#160;      Col [next_col].shared3.prev = Empty ;</div>
<div class="line"><a name="l01037"></a><span class="lineno"> 1037</span>&#160;    }</div>
<div class="line"><a name="l01038"></a><span class="lineno"> 1038</span>&#160; </div>
<div class="line"><a name="l01039"></a><span class="lineno"> 1039</span>&#160;    COLAMD_ASSERT (Col[pivot_col].is_alive()) ;</div>
<div class="line"><a name="l01040"></a><span class="lineno"> 1040</span>&#160;    COLAMD_DEBUG3 ((<span class="stringliteral">&quot;Pivot col: %d\n&quot;</span>, pivot_col)) ;</div>
<div class="line"><a name="l01041"></a><span class="lineno"> 1041</span>&#160; </div>
<div class="line"><a name="l01042"></a><span class="lineno"> 1042</span>&#160;    <span class="comment">/* remember score for defrag check */</span></div>
<div class="line"><a name="l01043"></a><span class="lineno"> 1043</span>&#160;    pivot_col_score = Col [pivot_col].shared2.score ;</div>
<div class="line"><a name="l01044"></a><span class="lineno"> 1044</span>&#160; </div>
<div class="line"><a name="l01045"></a><span class="lineno"> 1045</span>&#160;    <span class="comment">/* the pivot column is the kth column in the pivot order */</span></div>
<div class="line"><a name="l01046"></a><span class="lineno"> 1046</span>&#160;    Col [pivot_col].shared2.order = k ;</div>
<div class="line"><a name="l01047"></a><span class="lineno"> 1047</span>&#160; </div>
<div class="line"><a name="l01048"></a><span class="lineno"> 1048</span>&#160;    <span class="comment">/* increment order count by column thickness */</span></div>
<div class="line"><a name="l01049"></a><span class="lineno"> 1049</span>&#160;    pivot_col_thickness = Col [pivot_col].shared1.thickness ;</div>
<div class="line"><a name="l01050"></a><span class="lineno"> 1050</span>&#160;    k += pivot_col_thickness ;</div>
<div class="line"><a name="l01051"></a><span class="lineno"> 1051</span>&#160;    COLAMD_ASSERT (pivot_col_thickness &gt; 0) ;</div>
<div class="line"><a name="l01052"></a><span class="lineno"> 1052</span>&#160; </div>
<div class="line"><a name="l01053"></a><span class="lineno"> 1053</span>&#160;    <span class="comment">/* === Garbage_collection, if necessary ============================= */</span></div>
<div class="line"><a name="l01054"></a><span class="lineno"> 1054</span>&#160; </div>
<div class="line"><a name="l01055"></a><span class="lineno"> 1055</span>&#160;    needed_memory = numext::mini(pivot_col_score, n_col - k) ;</div>
<div class="line"><a name="l01056"></a><span class="lineno"> 1056</span>&#160;    <span class="keywordflow">if</span> (pfree + needed_memory &gt;= Alen)</div>
<div class="line"><a name="l01057"></a><span class="lineno"> 1057</span>&#160;    {</div>
<div class="line"><a name="l01058"></a><span class="lineno"> 1058</span>&#160;      pfree = Colamd::garbage_collection (n_row, n_col, Row, Col, A, &amp;A [pfree]) ;</div>
<div class="line"><a name="l01059"></a><span class="lineno"> 1059</span>&#160;      ngarbage++ ;</div>
<div class="line"><a name="l01060"></a><span class="lineno"> 1060</span>&#160;      <span class="comment">/* after garbage collection we will have enough */</span></div>
<div class="line"><a name="l01061"></a><span class="lineno"> 1061</span>&#160;      COLAMD_ASSERT (pfree + needed_memory &lt; Alen) ;</div>
<div class="line"><a name="l01062"></a><span class="lineno"> 1062</span>&#160;      <span class="comment">/* garbage collection has wiped out the Row[].shared2.mark array */</span></div>
<div class="line"><a name="l01063"></a><span class="lineno"> 1063</span>&#160;      tag_mark = Colamd::clear_mark (n_row, Row) ;</div>
<div class="line"><a name="l01064"></a><span class="lineno"> 1064</span>&#160; </div>
<div class="line"><a name="l01065"></a><span class="lineno"> 1065</span>&#160;    }</div>
<div class="line"><a name="l01066"></a><span class="lineno"> 1066</span>&#160; </div>
<div class="line"><a name="l01067"></a><span class="lineno"> 1067</span>&#160;    <span class="comment">/* === Compute pivot row pattern ==================================== */</span></div>
<div class="line"><a name="l01068"></a><span class="lineno"> 1068</span>&#160; </div>
<div class="line"><a name="l01069"></a><span class="lineno"> 1069</span>&#160;    <span class="comment">/* get starting location for this new merged row */</span></div>
<div class="line"><a name="l01070"></a><span class="lineno"> 1070</span>&#160;    pivot_row_start = pfree ;</div>
<div class="line"><a name="l01071"></a><span class="lineno"> 1071</span>&#160; </div>
<div class="line"><a name="l01072"></a><span class="lineno"> 1072</span>&#160;    <span class="comment">/* initialize new row counts to zero */</span></div>
<div class="line"><a name="l01073"></a><span class="lineno"> 1073</span>&#160;    pivot_row_degree = 0 ;</div>
<div class="line"><a name="l01074"></a><span class="lineno"> 1074</span>&#160; </div>
<div class="line"><a name="l01075"></a><span class="lineno"> 1075</span>&#160;    <span class="comment">/* tag pivot column as having been visited so it isn&#39;t included */</span></div>
<div class="line"><a name="l01076"></a><span class="lineno"> 1076</span>&#160;    <span class="comment">/* in merged pivot row */</span></div>
<div class="line"><a name="l01077"></a><span class="lineno"> 1077</span>&#160;    Col [pivot_col].shared1.thickness = -pivot_col_thickness ;</div>
<div class="line"><a name="l01078"></a><span class="lineno"> 1078</span>&#160; </div>
<div class="line"><a name="l01079"></a><span class="lineno"> 1079</span>&#160;    <span class="comment">/* pivot row is the union of all rows in the pivot column pattern */</span></div>
<div class="line"><a name="l01080"></a><span class="lineno"> 1080</span>&#160;    cp = &amp;A [Col [pivot_col].start] ;</div>
<div class="line"><a name="l01081"></a><span class="lineno"> 1081</span>&#160;    cp_end = cp + Col [pivot_col].length ;</div>
<div class="line"><a name="l01082"></a><span class="lineno"> 1082</span>&#160;    <span class="keywordflow">while</span> (cp &lt; cp_end)</div>
<div class="line"><a name="l01083"></a><span class="lineno"> 1083</span>&#160;    {</div>
<div class="line"><a name="l01084"></a><span class="lineno"> 1084</span>&#160;      <span class="comment">/* get a row */</span></div>
<div class="line"><a name="l01085"></a><span class="lineno"> 1085</span>&#160;      row = *cp++ ;</div>
<div class="line"><a name="l01086"></a><span class="lineno"> 1086</span>&#160;      COLAMD_DEBUG4 ((<span class="stringliteral">&quot;Pivot col pattern %d %d\n&quot;</span>, Row[row].is_alive(), row)) ;</div>
<div class="line"><a name="l01087"></a><span class="lineno"> 1087</span>&#160;      <span class="comment">/* skip if row is dead */</span></div>
<div class="line"><a name="l01088"></a><span class="lineno"> 1088</span>&#160;      <span class="keywordflow">if</span> (Row[row].is_dead())</div>
<div class="line"><a name="l01089"></a><span class="lineno"> 1089</span>&#160;      {</div>
<div class="line"><a name="l01090"></a><span class="lineno"> 1090</span>&#160;        continue ;</div>
<div class="line"><a name="l01091"></a><span class="lineno"> 1091</span>&#160;      }</div>
<div class="line"><a name="l01092"></a><span class="lineno"> 1092</span>&#160;      rp = &amp;A [Row [row].start] ;</div>
<div class="line"><a name="l01093"></a><span class="lineno"> 1093</span>&#160;      rp_end = rp + Row [row].length ;</div>
<div class="line"><a name="l01094"></a><span class="lineno"> 1094</span>&#160;      <span class="keywordflow">while</span> (rp &lt; rp_end)</div>
<div class="line"><a name="l01095"></a><span class="lineno"> 1095</span>&#160;      {</div>
<div class="line"><a name="l01096"></a><span class="lineno"> 1096</span>&#160;        <span class="comment">/* get a column */</span></div>
<div class="line"><a name="l01097"></a><span class="lineno"> 1097</span>&#160;        col = *rp++ ;</div>
<div class="line"><a name="l01098"></a><span class="lineno"> 1098</span>&#160;        <span class="comment">/* add the column, if alive and untagged */</span></div>
<div class="line"><a name="l01099"></a><span class="lineno"> 1099</span>&#160;        col_thickness = Col [col].shared1.thickness ;</div>
<div class="line"><a name="l01100"></a><span class="lineno"> 1100</span>&#160;        <span class="keywordflow">if</span> (col_thickness &gt; 0 &amp;&amp; Col[col].is_alive())</div>
<div class="line"><a name="l01101"></a><span class="lineno"> 1101</span>&#160;        {</div>
<div class="line"><a name="l01102"></a><span class="lineno"> 1102</span>&#160;          <span class="comment">/* tag column in pivot row */</span></div>
<div class="line"><a name="l01103"></a><span class="lineno"> 1103</span>&#160;          Col [col].shared1.thickness = -col_thickness ;</div>
<div class="line"><a name="l01104"></a><span class="lineno"> 1104</span>&#160;          COLAMD_ASSERT (pfree &lt; Alen) ;</div>
<div class="line"><a name="l01105"></a><span class="lineno"> 1105</span>&#160;          <span class="comment">/* place column in pivot row */</span></div>
<div class="line"><a name="l01106"></a><span class="lineno"> 1106</span>&#160;          A [pfree++] = col ;</div>
<div class="line"><a name="l01107"></a><span class="lineno"> 1107</span>&#160;          pivot_row_degree += col_thickness ;</div>
<div class="line"><a name="l01108"></a><span class="lineno"> 1108</span>&#160;        }</div>
<div class="line"><a name="l01109"></a><span class="lineno"> 1109</span>&#160;      }</div>
<div class="line"><a name="l01110"></a><span class="lineno"> 1110</span>&#160;    }</div>
<div class="line"><a name="l01111"></a><span class="lineno"> 1111</span>&#160; </div>
<div class="line"><a name="l01112"></a><span class="lineno"> 1112</span>&#160;    <span class="comment">/* clear tag on pivot column */</span></div>
<div class="line"><a name="l01113"></a><span class="lineno"> 1113</span>&#160;    Col [pivot_col].shared1.thickness = pivot_col_thickness ;</div>
<div class="line"><a name="l01114"></a><span class="lineno"> 1114</span>&#160;    max_deg = numext::maxi(max_deg, pivot_row_degree) ;</div>
<div class="line"><a name="l01115"></a><span class="lineno"> 1115</span>&#160; </div>
<div class="line"><a name="l01116"></a><span class="lineno"> 1116</span>&#160; </div>
<div class="line"><a name="l01117"></a><span class="lineno"> 1117</span>&#160;    <span class="comment">/* === Kill all rows used to construct pivot row ==================== */</span></div>
<div class="line"><a name="l01118"></a><span class="lineno"> 1118</span>&#160; </div>
<div class="line"><a name="l01119"></a><span class="lineno"> 1119</span>&#160;    <span class="comment">/* also kill pivot row, temporarily */</span></div>
<div class="line"><a name="l01120"></a><span class="lineno"> 1120</span>&#160;    cp = &amp;A [Col [pivot_col].start] ;</div>
<div class="line"><a name="l01121"></a><span class="lineno"> 1121</span>&#160;    cp_end = cp + Col [pivot_col].length ;</div>
<div class="line"><a name="l01122"></a><span class="lineno"> 1122</span>&#160;    <span class="keywordflow">while</span> (cp &lt; cp_end)</div>
<div class="line"><a name="l01123"></a><span class="lineno"> 1123</span>&#160;    {</div>
<div class="line"><a name="l01124"></a><span class="lineno"> 1124</span>&#160;      <span class="comment">/* may be killing an already dead row */</span></div>
<div class="line"><a name="l01125"></a><span class="lineno"> 1125</span>&#160;      row = *cp++ ;</div>
<div class="line"><a name="l01126"></a><span class="lineno"> 1126</span>&#160;      COLAMD_DEBUG3 ((<span class="stringliteral">&quot;Kill row in pivot col: %d\n&quot;</span>, row)) ;</div>
<div class="line"><a name="l01127"></a><span class="lineno"> 1127</span>&#160;      Row[row].kill() ;</div>
<div class="line"><a name="l01128"></a><span class="lineno"> 1128</span>&#160;    }</div>
<div class="line"><a name="l01129"></a><span class="lineno"> 1129</span>&#160; </div>
<div class="line"><a name="l01130"></a><span class="lineno"> 1130</span>&#160;    <span class="comment">/* === Select a row index to use as the new pivot row =============== */</span></div>
<div class="line"><a name="l01131"></a><span class="lineno"> 1131</span>&#160; </div>
<div class="line"><a name="l01132"></a><span class="lineno"> 1132</span>&#160;    pivot_row_length = pfree - pivot_row_start ;</div>
<div class="line"><a name="l01133"></a><span class="lineno"> 1133</span>&#160;    <span class="keywordflow">if</span> (pivot_row_length &gt; 0)</div>
<div class="line"><a name="l01134"></a><span class="lineno"> 1134</span>&#160;    {</div>
<div class="line"><a name="l01135"></a><span class="lineno"> 1135</span>&#160;      <span class="comment">/* pick the &quot;pivot&quot; row arbitrarily (first row in col) */</span></div>
<div class="line"><a name="l01136"></a><span class="lineno"> 1136</span>&#160;      pivot_row = A [Col [pivot_col].start] ;</div>
<div class="line"><a name="l01137"></a><span class="lineno"> 1137</span>&#160;      COLAMD_DEBUG3 ((<span class="stringliteral">&quot;Pivotal row is %d\n&quot;</span>, pivot_row)) ;</div>
<div class="line"><a name="l01138"></a><span class="lineno"> 1138</span>&#160;    }</div>
<div class="line"><a name="l01139"></a><span class="lineno"> 1139</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l01140"></a><span class="lineno"> 1140</span>&#160;    {</div>
<div class="line"><a name="l01141"></a><span class="lineno"> 1141</span>&#160;      <span class="comment">/* there is no pivot row, since it is of zero length */</span></div>
<div class="line"><a name="l01142"></a><span class="lineno"> 1142</span>&#160;      pivot_row = Empty ;</div>
<div class="line"><a name="l01143"></a><span class="lineno"> 1143</span>&#160;      COLAMD_ASSERT (pivot_row_length == 0) ;</div>
<div class="line"><a name="l01144"></a><span class="lineno"> 1144</span>&#160;    }</div>
<div class="line"><a name="l01145"></a><span class="lineno"> 1145</span>&#160;    COLAMD_ASSERT (Col [pivot_col].length &gt; 0 || pivot_row_length == 0) ;</div>
<div class="line"><a name="l01146"></a><span class="lineno"> 1146</span>&#160; </div>
<div class="line"><a name="l01147"></a><span class="lineno"> 1147</span>&#160;    <span class="comment">/* === Approximate degree computation =============================== */</span></div>
<div class="line"><a name="l01148"></a><span class="lineno"> 1148</span>&#160; </div>
<div class="line"><a name="l01149"></a><span class="lineno"> 1149</span>&#160;    <span class="comment">/* Here begins the computation of the approximate degree.  The column */</span></div>
<div class="line"><a name="l01150"></a><span class="lineno"> 1150</span>&#160;    <span class="comment">/* score is the sum of the pivot row &quot;length&quot;, plus the size of the */</span></div>
<div class="line"><a name="l01151"></a><span class="lineno"> 1151</span>&#160;    <span class="comment">/* set differences of each row in the column minus the pattern of the */</span></div>
<div class="line"><a name="l01152"></a><span class="lineno"> 1152</span>&#160;    <span class="comment">/* pivot row itself.  The column (&quot;thickness&quot;) itself is also */</span></div>
<div class="line"><a name="l01153"></a><span class="lineno"> 1153</span>&#160;    <span class="comment">/* excluded from the column score (we thus use an approximate */</span></div>
<div class="line"><a name="l01154"></a><span class="lineno"> 1154</span>&#160;    <span class="comment">/* external degree). */</span></div>
<div class="line"><a name="l01155"></a><span class="lineno"> 1155</span>&#160; </div>
<div class="line"><a name="l01156"></a><span class="lineno"> 1156</span>&#160;    <span class="comment">/* The time taken by the following code (compute set differences, and */</span></div>
<div class="line"><a name="l01157"></a><span class="lineno"> 1157</span>&#160;    <span class="comment">/* add them up) is proportional to the size of the data structure */</span></div>
<div class="line"><a name="l01158"></a><span class="lineno"> 1158</span>&#160;    <span class="comment">/* being scanned - that is, the sum of the sizes of each column in */</span></div>
<div class="line"><a name="l01159"></a><span class="lineno"> 1159</span>&#160;    <span class="comment">/* the pivot row.  Thus, the amortized time to compute a column score */</span></div>
<div class="line"><a name="l01160"></a><span class="lineno"> 1160</span>&#160;    <span class="comment">/* is proportional to the size of that column (where size, in this */</span></div>
<div class="line"><a name="l01161"></a><span class="lineno"> 1161</span>&#160;    <span class="comment">/* context, is the column &quot;length&quot;, or the number of row indices */</span></div>
<div class="line"><a name="l01162"></a><span class="lineno"> 1162</span>&#160;    <span class="comment">/* in that column).  The number of row indices in a column is */</span></div>
<div class="line"><a name="l01163"></a><span class="lineno"> 1163</span>&#160;    <span class="comment">/* monotonically non-decreasing, from the length of the original */</span></div>
<div class="line"><a name="l01164"></a><span class="lineno"> 1164</span>&#160;    <span class="comment">/* column on input to colamd. */</span></div>
<div class="line"><a name="l01165"></a><span class="lineno"> 1165</span>&#160; </div>
<div class="line"><a name="l01166"></a><span class="lineno"> 1166</span>&#160;    <span class="comment">/* === Compute set differences ====================================== */</span></div>
<div class="line"><a name="l01167"></a><span class="lineno"> 1167</span>&#160; </div>
<div class="line"><a name="l01168"></a><span class="lineno"> 1168</span>&#160;    COLAMD_DEBUG3 ((<span class="stringliteral">&quot;** Computing set differences phase. **\n&quot;</span>)) ;</div>
<div class="line"><a name="l01169"></a><span class="lineno"> 1169</span>&#160; </div>
<div class="line"><a name="l01170"></a><span class="lineno"> 1170</span>&#160;    <span class="comment">/* pivot row is currently dead - it will be revived later. */</span></div>
<div class="line"><a name="l01171"></a><span class="lineno"> 1171</span>&#160; </div>
<div class="line"><a name="l01172"></a><span class="lineno"> 1172</span>&#160;    COLAMD_DEBUG3 ((<span class="stringliteral">&quot;Pivot row: &quot;</span>)) ;</div>
<div class="line"><a name="l01173"></a><span class="lineno"> 1173</span>&#160;    <span class="comment">/* for each column in pivot row */</span></div>
<div class="line"><a name="l01174"></a><span class="lineno"> 1174</span>&#160;    rp = &amp;A [pivot_row_start] ;</div>
<div class="line"><a name="l01175"></a><span class="lineno"> 1175</span>&#160;    rp_end = rp + pivot_row_length ;</div>
<div class="line"><a name="l01176"></a><span class="lineno"> 1176</span>&#160;    <span class="keywordflow">while</span> (rp &lt; rp_end)</div>
<div class="line"><a name="l01177"></a><span class="lineno"> 1177</span>&#160;    {</div>
<div class="line"><a name="l01178"></a><span class="lineno"> 1178</span>&#160;      col = *rp++ ;</div>
<div class="line"><a name="l01179"></a><span class="lineno"> 1179</span>&#160;      COLAMD_ASSERT (Col[col].is_alive() &amp;&amp; col != pivot_col) ;</div>
<div class="line"><a name="l01180"></a><span class="lineno"> 1180</span>&#160;      COLAMD_DEBUG3 ((<span class="stringliteral">&quot;Col: %d\n&quot;</span>, col)) ;</div>
<div class="line"><a name="l01181"></a><span class="lineno"> 1181</span>&#160; </div>
<div class="line"><a name="l01182"></a><span class="lineno"> 1182</span>&#160;      <span class="comment">/* clear tags used to construct pivot row pattern */</span></div>
<div class="line"><a name="l01183"></a><span class="lineno"> 1183</span>&#160;      col_thickness = -Col [col].shared1.thickness ;</div>
<div class="line"><a name="l01184"></a><span class="lineno"> 1184</span>&#160;      COLAMD_ASSERT (col_thickness &gt; 0) ;</div>
<div class="line"><a name="l01185"></a><span class="lineno"> 1185</span>&#160;      Col [col].shared1.thickness = col_thickness ;</div>
<div class="line"><a name="l01186"></a><span class="lineno"> 1186</span>&#160; </div>
<div class="line"><a name="l01187"></a><span class="lineno"> 1187</span>&#160;      <span class="comment">/* === Remove column from degree list =========================== */</span></div>
<div class="line"><a name="l01188"></a><span class="lineno"> 1188</span>&#160; </div>
<div class="line"><a name="l01189"></a><span class="lineno"> 1189</span>&#160;      cur_score = Col [col].shared2.score ;</div>
<div class="line"><a name="l01190"></a><span class="lineno"> 1190</span>&#160;      prev_col = Col [col].shared3.prev ;</div>
<div class="line"><a name="l01191"></a><span class="lineno"> 1191</span>&#160;      next_col = Col [col].shared4.degree_next ;</div>
<div class="line"><a name="l01192"></a><span class="lineno"> 1192</span>&#160;      COLAMD_ASSERT (cur_score &gt;= 0) ;</div>
<div class="line"><a name="l01193"></a><span class="lineno"> 1193</span>&#160;      COLAMD_ASSERT (cur_score &lt;= n_col) ;</div>
<div class="line"><a name="l01194"></a><span class="lineno"> 1194</span>&#160;      COLAMD_ASSERT (cur_score &gt;= Empty) ;</div>
<div class="line"><a name="l01195"></a><span class="lineno"> 1195</span>&#160;      <span class="keywordflow">if</span> (prev_col == Empty)</div>
<div class="line"><a name="l01196"></a><span class="lineno"> 1196</span>&#160;      {</div>
<div class="line"><a name="l01197"></a><span class="lineno"> 1197</span>&#160;        head [cur_score] = next_col ;</div>
<div class="line"><a name="l01198"></a><span class="lineno"> 1198</span>&#160;      }</div>
<div class="line"><a name="l01199"></a><span class="lineno"> 1199</span>&#160;      <span class="keywordflow">else</span></div>
<div class="line"><a name="l01200"></a><span class="lineno"> 1200</span>&#160;      {</div>
<div class="line"><a name="l01201"></a><span class="lineno"> 1201</span>&#160;        Col [prev_col].shared4.degree_next = next_col ;</div>
<div class="line"><a name="l01202"></a><span class="lineno"> 1202</span>&#160;      }</div>
<div class="line"><a name="l01203"></a><span class="lineno"> 1203</span>&#160;      <span class="keywordflow">if</span> (next_col != Empty)</div>
<div class="line"><a name="l01204"></a><span class="lineno"> 1204</span>&#160;      {</div>
<div class="line"><a name="l01205"></a><span class="lineno"> 1205</span>&#160;        Col [next_col].shared3.prev = prev_col ;</div>
<div class="line"><a name="l01206"></a><span class="lineno"> 1206</span>&#160;      }</div>
<div class="line"><a name="l01207"></a><span class="lineno"> 1207</span>&#160; </div>
<div class="line"><a name="l01208"></a><span class="lineno"> 1208</span>&#160;      <span class="comment">/* === Scan the column ========================================== */</span></div>
<div class="line"><a name="l01209"></a><span class="lineno"> 1209</span>&#160; </div>
<div class="line"><a name="l01210"></a><span class="lineno"> 1210</span>&#160;      cp = &amp;A [Col [col].start] ;</div>
<div class="line"><a name="l01211"></a><span class="lineno"> 1211</span>&#160;      cp_end = cp + Col [col].length ;</div>
<div class="line"><a name="l01212"></a><span class="lineno"> 1212</span>&#160;      <span class="keywordflow">while</span> (cp &lt; cp_end)</div>
<div class="line"><a name="l01213"></a><span class="lineno"> 1213</span>&#160;      {</div>
<div class="line"><a name="l01214"></a><span class="lineno"> 1214</span>&#160;        <span class="comment">/* get a row */</span></div>
<div class="line"><a name="l01215"></a><span class="lineno"> 1215</span>&#160;        row = *cp++ ;</div>
<div class="line"><a name="l01216"></a><span class="lineno"> 1216</span>&#160;        <span class="comment">/* skip if dead */</span></div>
<div class="line"><a name="l01217"></a><span class="lineno"> 1217</span>&#160;        <span class="keywordflow">if</span> (Row[row].is_dead())</div>
<div class="line"><a name="l01218"></a><span class="lineno"> 1218</span>&#160;        {</div>
<div class="line"><a name="l01219"></a><span class="lineno"> 1219</span>&#160;          continue ;</div>
<div class="line"><a name="l01220"></a><span class="lineno"> 1220</span>&#160;        }</div>
<div class="line"><a name="l01221"></a><span class="lineno"> 1221</span>&#160;  row_mark = Row [row].shared2.mark ;</div>
<div class="line"><a name="l01222"></a><span class="lineno"> 1222</span>&#160;        COLAMD_ASSERT (row != pivot_row) ;</div>
<div class="line"><a name="l01223"></a><span class="lineno"> 1223</span>&#160;        set_difference = row_mark - tag_mark ;</div>
<div class="line"><a name="l01224"></a><span class="lineno"> 1224</span>&#160;        <span class="comment">/* check if the row has been seen yet */</span></div>
<div class="line"><a name="l01225"></a><span class="lineno"> 1225</span>&#160;        <span class="keywordflow">if</span> (set_difference &lt; 0)</div>
<div class="line"><a name="l01226"></a><span class="lineno"> 1226</span>&#160;        {</div>
<div class="line"><a name="l01227"></a><span class="lineno"> 1227</span>&#160;          COLAMD_ASSERT (Row [row].shared1.degree &lt;= max_deg) ;</div>
<div class="line"><a name="l01228"></a><span class="lineno"> 1228</span>&#160;          set_difference = Row [row].shared1.degree ;</div>
<div class="line"><a name="l01229"></a><span class="lineno"> 1229</span>&#160;        }</div>
<div class="line"><a name="l01230"></a><span class="lineno"> 1230</span>&#160;        <span class="comment">/* subtract column thickness from this row&#39;s set difference */</span></div>
<div class="line"><a name="l01231"></a><span class="lineno"> 1231</span>&#160;        set_difference -= col_thickness ;</div>
<div class="line"><a name="l01232"></a><span class="lineno"> 1232</span>&#160;        COLAMD_ASSERT (set_difference &gt;= 0) ;</div>
<div class="line"><a name="l01233"></a><span class="lineno"> 1233</span>&#160;        <span class="comment">/* absorb this row if the set difference becomes zero */</span></div>
<div class="line"><a name="l01234"></a><span class="lineno"> 1234</span>&#160;        <span class="keywordflow">if</span> (set_difference == 0)</div>
<div class="line"><a name="l01235"></a><span class="lineno"> 1235</span>&#160;        {</div>
<div class="line"><a name="l01236"></a><span class="lineno"> 1236</span>&#160;          COLAMD_DEBUG3 ((<span class="stringliteral">&quot;aggressive absorption. Row: %d\n&quot;</span>, row)) ;</div>
<div class="line"><a name="l01237"></a><span class="lineno"> 1237</span>&#160;          Row[row].kill() ;</div>
<div class="line"><a name="l01238"></a><span class="lineno"> 1238</span>&#160;        }</div>
<div class="line"><a name="l01239"></a><span class="lineno"> 1239</span>&#160;        <span class="keywordflow">else</span></div>
<div class="line"><a name="l01240"></a><span class="lineno"> 1240</span>&#160;        {</div>
<div class="line"><a name="l01241"></a><span class="lineno"> 1241</span>&#160;          <span class="comment">/* save the new mark */</span></div>
<div class="line"><a name="l01242"></a><span class="lineno"> 1242</span>&#160;          Row [row].shared2.mark = set_difference + tag_mark ;</div>
<div class="line"><a name="l01243"></a><span class="lineno"> 1243</span>&#160;        }</div>
<div class="line"><a name="l01244"></a><span class="lineno"> 1244</span>&#160;      }</div>
<div class="line"><a name="l01245"></a><span class="lineno"> 1245</span>&#160;    }</div>
<div class="line"><a name="l01246"></a><span class="lineno"> 1246</span>&#160; </div>
<div class="line"><a name="l01247"></a><span class="lineno"> 1247</span>&#160; </div>
<div class="line"><a name="l01248"></a><span class="lineno"> 1248</span>&#160;    <span class="comment">/* === Add up set differences for each column ======================= */</span></div>
<div class="line"><a name="l01249"></a><span class="lineno"> 1249</span>&#160; </div>
<div class="line"><a name="l01250"></a><span class="lineno"> 1250</span>&#160;    COLAMD_DEBUG3 ((<span class="stringliteral">&quot;** Adding set differences phase. **\n&quot;</span>)) ;</div>
<div class="line"><a name="l01251"></a><span class="lineno"> 1251</span>&#160; </div>
<div class="line"><a name="l01252"></a><span class="lineno"> 1252</span>&#160;    <span class="comment">/* for each column in pivot row */</span></div>
<div class="line"><a name="l01253"></a><span class="lineno"> 1253</span>&#160;    rp = &amp;A [pivot_row_start] ;</div>
<div class="line"><a name="l01254"></a><span class="lineno"> 1254</span>&#160;    rp_end = rp + pivot_row_length ;</div>
<div class="line"><a name="l01255"></a><span class="lineno"> 1255</span>&#160;    <span class="keywordflow">while</span> (rp &lt; rp_end)</div>
<div class="line"><a name="l01256"></a><span class="lineno"> 1256</span>&#160;    {</div>
<div class="line"><a name="l01257"></a><span class="lineno"> 1257</span>&#160;      <span class="comment">/* get a column */</span></div>
<div class="line"><a name="l01258"></a><span class="lineno"> 1258</span>&#160;      col = *rp++ ;</div>
<div class="line"><a name="l01259"></a><span class="lineno"> 1259</span>&#160;      COLAMD_ASSERT (Col[col].is_alive() &amp;&amp; col != pivot_col) ;</div>
<div class="line"><a name="l01260"></a><span class="lineno"> 1260</span>&#160;      hash = 0 ;</div>
<div class="line"><a name="l01261"></a><span class="lineno"> 1261</span>&#160;      cur_score = 0 ;</div>
<div class="line"><a name="l01262"></a><span class="lineno"> 1262</span>&#160;      cp = &amp;A [Col [col].start] ;</div>
<div class="line"><a name="l01263"></a><span class="lineno"> 1263</span>&#160;      <span class="comment">/* compact the column */</span></div>
<div class="line"><a name="l01264"></a><span class="lineno"> 1264</span>&#160;      new_cp = cp ;</div>
<div class="line"><a name="l01265"></a><span class="lineno"> 1265</span>&#160;      cp_end = cp + Col [col].length ;</div>
<div class="line"><a name="l01266"></a><span class="lineno"> 1266</span>&#160; </div>
<div class="line"><a name="l01267"></a><span class="lineno"> 1267</span>&#160;      COLAMD_DEBUG4 ((<span class="stringliteral">&quot;Adding set diffs for Col: %d.\n&quot;</span>, col)) ;</div>
<div class="line"><a name="l01268"></a><span class="lineno"> 1268</span>&#160; </div>
<div class="line"><a name="l01269"></a><span class="lineno"> 1269</span>&#160;      <span class="keywordflow">while</span> (cp &lt; cp_end)</div>
<div class="line"><a name="l01270"></a><span class="lineno"> 1270</span>&#160;      {</div>
<div class="line"><a name="l01271"></a><span class="lineno"> 1271</span>&#160;        <span class="comment">/* get a row */</span></div>
<div class="line"><a name="l01272"></a><span class="lineno"> 1272</span>&#160;        row = *cp++ ;</div>
<div class="line"><a name="l01273"></a><span class="lineno"> 1273</span>&#160;        COLAMD_ASSERT(row &gt;= 0 &amp;&amp; row &lt; n_row) ;</div>
<div class="line"><a name="l01274"></a><span class="lineno"> 1274</span>&#160;        <span class="comment">/* skip if dead */</span></div>
<div class="line"><a name="l01275"></a><span class="lineno"> 1275</span>&#160;        <span class="keywordflow">if</span> (Row [row].is_dead())</div>
<div class="line"><a name="l01276"></a><span class="lineno"> 1276</span>&#160;        {</div>
<div class="line"><a name="l01277"></a><span class="lineno"> 1277</span>&#160;          continue ;</div>
<div class="line"><a name="l01278"></a><span class="lineno"> 1278</span>&#160;        }</div>
<div class="line"><a name="l01279"></a><span class="lineno"> 1279</span>&#160;  row_mark = Row [row].shared2.mark ;</div>
<div class="line"><a name="l01280"></a><span class="lineno"> 1280</span>&#160;        COLAMD_ASSERT (row_mark &gt; tag_mark) ;</div>
<div class="line"><a name="l01281"></a><span class="lineno"> 1281</span>&#160;        <span class="comment">/* compact the column */</span></div>
<div class="line"><a name="l01282"></a><span class="lineno"> 1282</span>&#160;        *new_cp++ = row ;</div>
<div class="line"><a name="l01283"></a><span class="lineno"> 1283</span>&#160;        <span class="comment">/* compute hash function */</span></div>
<div class="line"><a name="l01284"></a><span class="lineno"> 1284</span>&#160;        hash += row ;</div>
<div class="line"><a name="l01285"></a><span class="lineno"> 1285</span>&#160;        <span class="comment">/* add set difference */</span></div>
<div class="line"><a name="l01286"></a><span class="lineno"> 1286</span>&#160;        cur_score += row_mark - tag_mark ;</div>
<div class="line"><a name="l01287"></a><span class="lineno"> 1287</span>&#160;        <span class="comment">/* integer overflow... */</span></div>
<div class="line"><a name="l01288"></a><span class="lineno"> 1288</span>&#160;        cur_score = numext::mini(cur_score, n_col) ;</div>
<div class="line"><a name="l01289"></a><span class="lineno"> 1289</span>&#160;      }</div>
<div class="line"><a name="l01290"></a><span class="lineno"> 1290</span>&#160; </div>
<div class="line"><a name="l01291"></a><span class="lineno"> 1291</span>&#160;      <span class="comment">/* recompute the column&#39;s length */</span></div>
<div class="line"><a name="l01292"></a><span class="lineno"> 1292</span>&#160;      Col [col].length = (IndexType) (new_cp - &amp;A [Col [col].start]) ;</div>
<div class="line"><a name="l01293"></a><span class="lineno"> 1293</span>&#160; </div>
<div class="line"><a name="l01294"></a><span class="lineno"> 1294</span>&#160;      <span class="comment">/* === Further mass elimination ================================= */</span></div>
<div class="line"><a name="l01295"></a><span class="lineno"> 1295</span>&#160; </div>
<div class="line"><a name="l01296"></a><span class="lineno"> 1296</span>&#160;      <span class="keywordflow">if</span> (Col [col].length == 0)</div>
<div class="line"><a name="l01297"></a><span class="lineno"> 1297</span>&#160;      {</div>
<div class="line"><a name="l01298"></a><span class="lineno"> 1298</span>&#160;        COLAMD_DEBUG4 ((<span class="stringliteral">&quot;further mass elimination. Col: %d\n&quot;</span>, col)) ;</div>
<div class="line"><a name="l01299"></a><span class="lineno"> 1299</span>&#160;        <span class="comment">/* nothing left but the pivot row in this column */</span></div>
<div class="line"><a name="l01300"></a><span class="lineno"> 1300</span>&#160;        Col[col].kill_principal() ;</div>
<div class="line"><a name="l01301"></a><span class="lineno"> 1301</span>&#160;        pivot_row_degree -= Col [col].shared1.thickness ;</div>
<div class="line"><a name="l01302"></a><span class="lineno"> 1302</span>&#160;        COLAMD_ASSERT (pivot_row_degree &gt;= 0) ;</div>
<div class="line"><a name="l01303"></a><span class="lineno"> 1303</span>&#160;        <span class="comment">/* order it */</span></div>
<div class="line"><a name="l01304"></a><span class="lineno"> 1304</span>&#160;        Col [col].shared2.order = k ;</div>
<div class="line"><a name="l01305"></a><span class="lineno"> 1305</span>&#160;        <span class="comment">/* increment order count by column thickness */</span></div>
<div class="line"><a name="l01306"></a><span class="lineno"> 1306</span>&#160;        k += Col [col].shared1.thickness ;</div>
<div class="line"><a name="l01307"></a><span class="lineno"> 1307</span>&#160;      }</div>
<div class="line"><a name="l01308"></a><span class="lineno"> 1308</span>&#160;      <span class="keywordflow">else</span></div>
<div class="line"><a name="l01309"></a><span class="lineno"> 1309</span>&#160;      {</div>
<div class="line"><a name="l01310"></a><span class="lineno"> 1310</span>&#160;        <span class="comment">/* === Prepare for supercolumn detection ==================== */</span></div>
<div class="line"><a name="l01311"></a><span class="lineno"> 1311</span>&#160; </div>
<div class="line"><a name="l01312"></a><span class="lineno"> 1312</span>&#160;        COLAMD_DEBUG4 ((<span class="stringliteral">&quot;Preparing supercol detection for Col: %d.\n&quot;</span>, col)) ;</div>
<div class="line"><a name="l01313"></a><span class="lineno"> 1313</span>&#160; </div>
<div class="line"><a name="l01314"></a><span class="lineno"> 1314</span>&#160;        <span class="comment">/* save score so far */</span></div>
<div class="line"><a name="l01315"></a><span class="lineno"> 1315</span>&#160;        Col [col].shared2.score = cur_score ;</div>
<div class="line"><a name="l01316"></a><span class="lineno"> 1316</span>&#160; </div>
<div class="line"><a name="l01317"></a><span class="lineno"> 1317</span>&#160;        <span class="comment">/* add column to hash table, for supercolumn detection */</span></div>
<div class="line"><a name="l01318"></a><span class="lineno"> 1318</span>&#160;        hash %= n_col + 1 ;</div>
<div class="line"><a name="l01319"></a><span class="lineno"> 1319</span>&#160; </div>
<div class="line"><a name="l01320"></a><span class="lineno"> 1320</span>&#160;        COLAMD_DEBUG4 ((<span class="stringliteral">&quot; Hash = %d, n_col = %d.\n&quot;</span>, hash, n_col)) ;</div>
<div class="line"><a name="l01321"></a><span class="lineno"> 1321</span>&#160;        COLAMD_ASSERT (hash &lt;= n_col) ;</div>
<div class="line"><a name="l01322"></a><span class="lineno"> 1322</span>&#160; </div>
<div class="line"><a name="l01323"></a><span class="lineno"> 1323</span>&#160;        head_column = head [hash] ;</div>
<div class="line"><a name="l01324"></a><span class="lineno"> 1324</span>&#160;        <span class="keywordflow">if</span> (head_column &gt; Empty)</div>
<div class="line"><a name="l01325"></a><span class="lineno"> 1325</span>&#160;        {</div>
<div class="line"><a name="l01326"></a><span class="lineno"> 1326</span>&#160;          <span class="comment">/* degree list &quot;hash&quot; is non-empty, use prev (shared3) of */</span></div>
<div class="line"><a name="l01327"></a><span class="lineno"> 1327</span>&#160;          <span class="comment">/* first column in degree list as head of hash bucket */</span></div>
<div class="line"><a name="l01328"></a><span class="lineno"> 1328</span>&#160;          first_col = Col [head_column].shared3.headhash ;</div>
<div class="line"><a name="l01329"></a><span class="lineno"> 1329</span>&#160;          Col [head_column].shared3.headhash = col ;</div>
<div class="line"><a name="l01330"></a><span class="lineno"> 1330</span>&#160;        }</div>
<div class="line"><a name="l01331"></a><span class="lineno"> 1331</span>&#160;        <span class="keywordflow">else</span></div>
<div class="line"><a name="l01332"></a><span class="lineno"> 1332</span>&#160;        {</div>
<div class="line"><a name="l01333"></a><span class="lineno"> 1333</span>&#160;          <span class="comment">/* degree list &quot;hash&quot; is empty, use head as hash bucket */</span></div>
<div class="line"><a name="l01334"></a><span class="lineno"> 1334</span>&#160;          first_col = - (head_column + 2) ;</div>
<div class="line"><a name="l01335"></a><span class="lineno"> 1335</span>&#160;          head [hash] = - (col + 2) ;</div>
<div class="line"><a name="l01336"></a><span class="lineno"> 1336</span>&#160;        }</div>
<div class="line"><a name="l01337"></a><span class="lineno"> 1337</span>&#160;        Col [col].shared4.hash_next = first_col ;</div>
<div class="line"><a name="l01338"></a><span class="lineno"> 1338</span>&#160; </div>
<div class="line"><a name="l01339"></a><span class="lineno"> 1339</span>&#160;        <span class="comment">/* save hash function in Col [col].shared3.hash */</span></div>
<div class="line"><a name="l01340"></a><span class="lineno"> 1340</span>&#160;        Col [col].shared3.hash = (IndexType) hash ;</div>
<div class="line"><a name="l01341"></a><span class="lineno"> 1341</span>&#160;        COLAMD_ASSERT (Col[col].is_alive()) ;</div>
<div class="line"><a name="l01342"></a><span class="lineno"> 1342</span>&#160;      }</div>
<div class="line"><a name="l01343"></a><span class="lineno"> 1343</span>&#160;    }</div>
<div class="line"><a name="l01344"></a><span class="lineno"> 1344</span>&#160; </div>
<div class="line"><a name="l01345"></a><span class="lineno"> 1345</span>&#160;    <span class="comment">/* The approximate external column degree is now computed.  */</span></div>
<div class="line"><a name="l01346"></a><span class="lineno"> 1346</span>&#160; </div>
<div class="line"><a name="l01347"></a><span class="lineno"> 1347</span>&#160;    <span class="comment">/* === Supercolumn detection ======================================== */</span></div>
<div class="line"><a name="l01348"></a><span class="lineno"> 1348</span>&#160; </div>
<div class="line"><a name="l01349"></a><span class="lineno"> 1349</span>&#160;    COLAMD_DEBUG3 ((<span class="stringliteral">&quot;** Supercolumn detection phase. **\n&quot;</span>)) ;</div>
<div class="line"><a name="l01350"></a><span class="lineno"> 1350</span>&#160; </div>
<div class="line"><a name="l01351"></a><span class="lineno"> 1351</span>&#160;    Colamd::detect_super_cols (Col, A, head, pivot_row_start, pivot_row_length) ;</div>
<div class="line"><a name="l01352"></a><span class="lineno"> 1352</span>&#160; </div>
<div class="line"><a name="l01353"></a><span class="lineno"> 1353</span>&#160;    <span class="comment">/* === Kill the pivotal column ====================================== */</span></div>
<div class="line"><a name="l01354"></a><span class="lineno"> 1354</span>&#160; </div>
<div class="line"><a name="l01355"></a><span class="lineno"> 1355</span>&#160;    Col[pivot_col].kill_principal() ;</div>
<div class="line"><a name="l01356"></a><span class="lineno"> 1356</span>&#160; </div>
<div class="line"><a name="l01357"></a><span class="lineno"> 1357</span>&#160;    <span class="comment">/* === Clear mark =================================================== */</span></div>
<div class="line"><a name="l01358"></a><span class="lineno"> 1358</span>&#160; </div>
<div class="line"><a name="l01359"></a><span class="lineno"> 1359</span>&#160;    tag_mark += (max_deg + 1) ;</div>
<div class="line"><a name="l01360"></a><span class="lineno"> 1360</span>&#160;    <span class="keywordflow">if</span> (tag_mark &gt;= max_mark)</div>
<div class="line"><a name="l01361"></a><span class="lineno"> 1361</span>&#160;    {</div>
<div class="line"><a name="l01362"></a><span class="lineno"> 1362</span>&#160;      COLAMD_DEBUG2 ((<span class="stringliteral">&quot;clearing tag_mark\n&quot;</span>)) ;</div>
<div class="line"><a name="l01363"></a><span class="lineno"> 1363</span>&#160;      tag_mark = Colamd::clear_mark (n_row, Row) ;</div>
<div class="line"><a name="l01364"></a><span class="lineno"> 1364</span>&#160;    }</div>
<div class="line"><a name="l01365"></a><span class="lineno"> 1365</span>&#160; </div>
<div class="line"><a name="l01366"></a><span class="lineno"> 1366</span>&#160;    <span class="comment">/* === Finalize the new pivot row, and column scores ================ */</span></div>
<div class="line"><a name="l01367"></a><span class="lineno"> 1367</span>&#160; </div>
<div class="line"><a name="l01368"></a><span class="lineno"> 1368</span>&#160;    COLAMD_DEBUG3 ((<span class="stringliteral">&quot;** Finalize scores phase. **\n&quot;</span>)) ;</div>
<div class="line"><a name="l01369"></a><span class="lineno"> 1369</span>&#160; </div>
<div class="line"><a name="l01370"></a><span class="lineno"> 1370</span>&#160;    <span class="comment">/* for each column in pivot row */</span></div>
<div class="line"><a name="l01371"></a><span class="lineno"> 1371</span>&#160;    rp = &amp;A [pivot_row_start] ;</div>
<div class="line"><a name="l01372"></a><span class="lineno"> 1372</span>&#160;    <span class="comment">/* compact the pivot row */</span></div>
<div class="line"><a name="l01373"></a><span class="lineno"> 1373</span>&#160;    new_rp = rp ;</div>
<div class="line"><a name="l01374"></a><span class="lineno"> 1374</span>&#160;    rp_end = rp + pivot_row_length ;</div>
<div class="line"><a name="l01375"></a><span class="lineno"> 1375</span>&#160;    <span class="keywordflow">while</span> (rp &lt; rp_end)</div>
<div class="line"><a name="l01376"></a><span class="lineno"> 1376</span>&#160;    {</div>
<div class="line"><a name="l01377"></a><span class="lineno"> 1377</span>&#160;      col = *rp++ ;</div>
<div class="line"><a name="l01378"></a><span class="lineno"> 1378</span>&#160;      <span class="comment">/* skip dead columns */</span></div>
<div class="line"><a name="l01379"></a><span class="lineno"> 1379</span>&#160;      <span class="keywordflow">if</span> (Col[col].is_dead())</div>
<div class="line"><a name="l01380"></a><span class="lineno"> 1380</span>&#160;      {</div>
<div class="line"><a name="l01381"></a><span class="lineno"> 1381</span>&#160;        continue ;</div>
<div class="line"><a name="l01382"></a><span class="lineno"> 1382</span>&#160;      }</div>
<div class="line"><a name="l01383"></a><span class="lineno"> 1383</span>&#160;      *new_rp++ = col ;</div>
<div class="line"><a name="l01384"></a><span class="lineno"> 1384</span>&#160;      <span class="comment">/* add new pivot row to column */</span></div>
<div class="line"><a name="l01385"></a><span class="lineno"> 1385</span>&#160;      A [Col [col].start + (Col [col].length++)] = pivot_row ;</div>
<div class="line"><a name="l01386"></a><span class="lineno"> 1386</span>&#160; </div>
<div class="line"><a name="l01387"></a><span class="lineno"> 1387</span>&#160;      <span class="comment">/* retrieve score so far and add on pivot row&#39;s degree. */</span></div>
<div class="line"><a name="l01388"></a><span class="lineno"> 1388</span>&#160;      <span class="comment">/* (we wait until here for this in case the pivot */</span></div>
<div class="line"><a name="l01389"></a><span class="lineno"> 1389</span>&#160;      <span class="comment">/* row&#39;s degree was reduced due to mass elimination). */</span></div>
<div class="line"><a name="l01390"></a><span class="lineno"> 1390</span>&#160;      cur_score = Col [col].shared2.score + pivot_row_degree ;</div>
<div class="line"><a name="l01391"></a><span class="lineno"> 1391</span>&#160; </div>
<div class="line"><a name="l01392"></a><span class="lineno"> 1392</span>&#160;      <span class="comment">/* calculate the max possible score as the number of */</span></div>
<div class="line"><a name="l01393"></a><span class="lineno"> 1393</span>&#160;      <span class="comment">/* external columns minus the &#39;k&#39; value minus the */</span></div>
<div class="line"><a name="l01394"></a><span class="lineno"> 1394</span>&#160;      <span class="comment">/* columns thickness */</span></div>
<div class="line"><a name="l01395"></a><span class="lineno"> 1395</span>&#160;      max_score = n_col - k - Col [col].shared1.thickness ;</div>
<div class="line"><a name="l01396"></a><span class="lineno"> 1396</span>&#160; </div>
<div class="line"><a name="l01397"></a><span class="lineno"> 1397</span>&#160;      <span class="comment">/* make the score the external degree of the union-of-rows */</span></div>
<div class="line"><a name="l01398"></a><span class="lineno"> 1398</span>&#160;      cur_score -= Col [col].shared1.thickness ;</div>
<div class="line"><a name="l01399"></a><span class="lineno"> 1399</span>&#160; </div>
<div class="line"><a name="l01400"></a><span class="lineno"> 1400</span>&#160;      <span class="comment">/* make sure score is less or equal than the max score */</span></div>
<div class="line"><a name="l01401"></a><span class="lineno"> 1401</span>&#160;      cur_score = numext::mini(cur_score, max_score) ;</div>
<div class="line"><a name="l01402"></a><span class="lineno"> 1402</span>&#160;      COLAMD_ASSERT (cur_score &gt;= 0) ;</div>
<div class="line"><a name="l01403"></a><span class="lineno"> 1403</span>&#160; </div>
<div class="line"><a name="l01404"></a><span class="lineno"> 1404</span>&#160;      <span class="comment">/* store updated score */</span></div>
<div class="line"><a name="l01405"></a><span class="lineno"> 1405</span>&#160;      Col [col].shared2.score = cur_score ;</div>
<div class="line"><a name="l01406"></a><span class="lineno"> 1406</span>&#160; </div>
<div class="line"><a name="l01407"></a><span class="lineno"> 1407</span>&#160;      <span class="comment">/* === Place column back in degree list ========================= */</span></div>
<div class="line"><a name="l01408"></a><span class="lineno"> 1408</span>&#160; </div>
<div class="line"><a name="l01409"></a><span class="lineno"> 1409</span>&#160;      COLAMD_ASSERT (min_score &gt;= 0) ;</div>
<div class="line"><a name="l01410"></a><span class="lineno"> 1410</span>&#160;      COLAMD_ASSERT (min_score &lt;= n_col) ;</div>
<div class="line"><a name="l01411"></a><span class="lineno"> 1411</span>&#160;      COLAMD_ASSERT (cur_score &gt;= 0) ;</div>
<div class="line"><a name="l01412"></a><span class="lineno"> 1412</span>&#160;      COLAMD_ASSERT (cur_score &lt;= n_col) ;</div>
<div class="line"><a name="l01413"></a><span class="lineno"> 1413</span>&#160;      COLAMD_ASSERT (head [cur_score] &gt;= Empty) ;</div>
<div class="line"><a name="l01414"></a><span class="lineno"> 1414</span>&#160;      next_col = head [cur_score] ;</div>
<div class="line"><a name="l01415"></a><span class="lineno"> 1415</span>&#160;      Col [col].shared4.degree_next = next_col ;</div>
<div class="line"><a name="l01416"></a><span class="lineno"> 1416</span>&#160;      Col [col].shared3.prev = Empty ;</div>
<div class="line"><a name="l01417"></a><span class="lineno"> 1417</span>&#160;      <span class="keywordflow">if</span> (next_col != Empty)</div>
<div class="line"><a name="l01418"></a><span class="lineno"> 1418</span>&#160;      {</div>
<div class="line"><a name="l01419"></a><span class="lineno"> 1419</span>&#160;        Col [next_col].shared3.prev = col ;</div>
<div class="line"><a name="l01420"></a><span class="lineno"> 1420</span>&#160;      }</div>
<div class="line"><a name="l01421"></a><span class="lineno"> 1421</span>&#160;      head [cur_score] = col ;</div>
<div class="line"><a name="l01422"></a><span class="lineno"> 1422</span>&#160; </div>
<div class="line"><a name="l01423"></a><span class="lineno"> 1423</span>&#160;      <span class="comment">/* see if this score is less than current min */</span></div>
<div class="line"><a name="l01424"></a><span class="lineno"> 1424</span>&#160;      min_score = numext::mini(min_score, cur_score) ;</div>
<div class="line"><a name="l01425"></a><span class="lineno"> 1425</span>&#160; </div>
<div class="line"><a name="l01426"></a><span class="lineno"> 1426</span>&#160;    }</div>
<div class="line"><a name="l01427"></a><span class="lineno"> 1427</span>&#160; </div>
<div class="line"><a name="l01428"></a><span class="lineno"> 1428</span>&#160;    <span class="comment">/* === Resurrect the new pivot row ================================== */</span></div>
<div class="line"><a name="l01429"></a><span class="lineno"> 1429</span>&#160; </div>
<div class="line"><a name="l01430"></a><span class="lineno"> 1430</span>&#160;    <span class="keywordflow">if</span> (pivot_row_degree &gt; 0)</div>
<div class="line"><a name="l01431"></a><span class="lineno"> 1431</span>&#160;    {</div>
<div class="line"><a name="l01432"></a><span class="lineno"> 1432</span>&#160;      <span class="comment">/* update pivot row length to reflect any cols that were killed */</span></div>
<div class="line"><a name="l01433"></a><span class="lineno"> 1433</span>&#160;      <span class="comment">/* during super-col detection and mass elimination */</span></div>
<div class="line"><a name="l01434"></a><span class="lineno"> 1434</span>&#160;      Row [pivot_row].start  = pivot_row_start ;</div>
<div class="line"><a name="l01435"></a><span class="lineno"> 1435</span>&#160;      Row [pivot_row].length = (IndexType) (new_rp - &amp;A[pivot_row_start]) ;</div>
<div class="line"><a name="l01436"></a><span class="lineno"> 1436</span>&#160;      Row [pivot_row].shared1.degree = pivot_row_degree ;</div>
<div class="line"><a name="l01437"></a><span class="lineno"> 1437</span>&#160;      Row [pivot_row].shared2.mark = 0 ;</div>
<div class="line"><a name="l01438"></a><span class="lineno"> 1438</span>&#160;      <span class="comment">/* pivot row is no longer dead */</span></div>
<div class="line"><a name="l01439"></a><span class="lineno"> 1439</span>&#160;    }</div>
<div class="line"><a name="l01440"></a><span class="lineno"> 1440</span>&#160;  }</div>
<div class="line"><a name="l01441"></a><span class="lineno"> 1441</span>&#160; </div>
<div class="line"><a name="l01442"></a><span class="lineno"> 1442</span>&#160;  <span class="comment">/* === All principal columns have now been ordered ====================== */</span></div>
<div class="line"><a name="l01443"></a><span class="lineno"> 1443</span>&#160; </div>
<div class="line"><a name="l01444"></a><span class="lineno"> 1444</span>&#160;  <span class="keywordflow">return</span> (ngarbage) ;</div>
<div class="line"><a name="l01445"></a><span class="lineno"> 1445</span>&#160;}</div>
<div class="line"><a name="l01446"></a><span class="lineno"> 1446</span>&#160; </div>
<div class="line"><a name="l01447"></a><span class="lineno"> 1447</span>&#160; </div>
<div class="line"><a name="l01448"></a><span class="lineno"> 1448</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01449"></a><span class="lineno"> 1449</span>&#160;<span class="comment">/* === order_children ======================================================= */</span></div>
<div class="line"><a name="l01450"></a><span class="lineno"> 1450</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01451"></a><span class="lineno"> 1451</span>&#160; </div>
<div class="line"><a name="l01452"></a><span class="lineno"> 1452</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l01453"></a><span class="lineno"> 1453</span>&#160;<span class="comment">  The find_ordering routine has ordered all of the principal columns (the</span></div>
<div class="line"><a name="l01454"></a><span class="lineno"> 1454</span>&#160;<span class="comment">  representatives of the supercolumns).  The non-principal columns have not</span></div>
<div class="line"><a name="l01455"></a><span class="lineno"> 1455</span>&#160;<span class="comment">  yet been ordered.  This routine orders those columns by walking up the</span></div>
<div class="line"><a name="l01456"></a><span class="lineno"> 1456</span>&#160;<span class="comment">  parent tree (a column is a child of the column which absorbed it).  The</span></div>
<div class="line"><a name="l01457"></a><span class="lineno"> 1457</span>&#160;<span class="comment">  final permutation vector is then placed in p [0 ... n_col-1], with p [0]</span></div>
<div class="line"><a name="l01458"></a><span class="lineno"> 1458</span>&#160;<span class="comment">  being the first column, and p [n_col-1] being the last.  It doesn&#39;t look</span></div>
<div class="line"><a name="l01459"></a><span class="lineno"> 1459</span>&#160;<span class="comment">  like it at first glance, but be assured that this routine takes time linear</span></div>
<div class="line"><a name="l01460"></a><span class="lineno"> 1460</span>&#160;<span class="comment">  in the number of columns.  Although not immediately obvious, the time</span></div>
<div class="line"><a name="l01461"></a><span class="lineno"> 1461</span>&#160;<span class="comment">  taken by this routine is O (n_col), that is, linear in the number of</span></div>
<div class="line"><a name="l01462"></a><span class="lineno"> 1462</span>&#160;<span class="comment">  columns.  Not user-callable.</span></div>
<div class="line"><a name="l01463"></a><span class="lineno"> 1463</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l01464"></a><span class="lineno"> 1464</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l01465"></a><span class="lineno"> 1465</span>&#160;<span class="keyword">static</span> <span class="keyword">inline</span>  <span class="keywordtype">void</span> order_children</div>
<div class="line"><a name="l01466"></a><span class="lineno"> 1466</span>&#160;(</div>
<div class="line"><a name="l01467"></a><span class="lineno"> 1467</span>&#160;  <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l01468"></a><span class="lineno"> 1468</span>&#160; </div>
<div class="line"><a name="l01469"></a><span class="lineno"> 1469</span>&#160;  IndexType n_col,      <span class="comment">/* number of columns of A */</span></div>
<div class="line"><a name="l01470"></a><span class="lineno"> 1470</span>&#160;  ColStructure&lt;IndexType&gt; Col [],    <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l01471"></a><span class="lineno"> 1471</span>&#160;  IndexType p []      <span class="comment">/* p [0 ... n_col-1] is the column permutation*/</span></div>
<div class="line"><a name="l01472"></a><span class="lineno"> 1472</span>&#160;  )</div>
<div class="line"><a name="l01473"></a><span class="lineno"> 1473</span>&#160;{</div>
<div class="line"><a name="l01474"></a><span class="lineno"> 1474</span>&#160;  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l01475"></a><span class="lineno"> 1475</span>&#160; </div>
<div class="line"><a name="l01476"></a><span class="lineno"> 1476</span>&#160;  IndexType i ;     <span class="comment">/* loop counter for all columns */</span></div>
<div class="line"><a name="l01477"></a><span class="lineno"> 1477</span>&#160;  IndexType c ;     <span class="comment">/* column index */</span></div>
<div class="line"><a name="l01478"></a><span class="lineno"> 1478</span>&#160;  IndexType parent ;    <span class="comment">/* index of column&#39;s parent */</span></div>
<div class="line"><a name="l01479"></a><span class="lineno"> 1479</span>&#160;  IndexType order ;     <span class="comment">/* column&#39;s order */</span></div>
<div class="line"><a name="l01480"></a><span class="lineno"> 1480</span>&#160; </div>
<div class="line"><a name="l01481"></a><span class="lineno"> 1481</span>&#160;  <span class="comment">/* === Order each non-principal column ================================== */</span></div>
<div class="line"><a name="l01482"></a><span class="lineno"> 1482</span>&#160; </div>
<div class="line"><a name="l01483"></a><span class="lineno"> 1483</span>&#160;  <span class="keywordflow">for</span> (i = 0 ; i &lt; n_col ; i++)</div>
<div class="line"><a name="l01484"></a><span class="lineno"> 1484</span>&#160;  {</div>
<div class="line"><a name="l01485"></a><span class="lineno"> 1485</span>&#160;    <span class="comment">/* find an un-ordered non-principal column */</span></div>
<div class="line"><a name="l01486"></a><span class="lineno"> 1486</span>&#160;    COLAMD_ASSERT (col_is_dead(Col, i)) ;</div>
<div class="line"><a name="l01487"></a><span class="lineno"> 1487</span>&#160;    <span class="keywordflow">if</span> (!Col[i].is_dead_principal() &amp;&amp; Col [i].shared2.order == Empty)</div>
<div class="line"><a name="l01488"></a><span class="lineno"> 1488</span>&#160;    {</div>
<div class="line"><a name="l01489"></a><span class="lineno"> 1489</span>&#160;      parent = i ;</div>
<div class="line"><a name="l01490"></a><span class="lineno"> 1490</span>&#160;      <span class="comment">/* once found, find its principal parent */</span></div>
<div class="line"><a name="l01491"></a><span class="lineno"> 1491</span>&#160;      <span class="keywordflow">do</span></div>
<div class="line"><a name="l01492"></a><span class="lineno"> 1492</span>&#160;      {</div>
<div class="line"><a name="l01493"></a><span class="lineno"> 1493</span>&#160;        parent = Col [parent].shared1.parent ;</div>
<div class="line"><a name="l01494"></a><span class="lineno"> 1494</span>&#160;      } <span class="keywordflow">while</span> (!Col[parent].is_dead_principal()) ;</div>
<div class="line"><a name="l01495"></a><span class="lineno"> 1495</span>&#160; </div>
<div class="line"><a name="l01496"></a><span class="lineno"> 1496</span>&#160;      <span class="comment">/* now, order all un-ordered non-principal columns along path */</span></div>
<div class="line"><a name="l01497"></a><span class="lineno"> 1497</span>&#160;      <span class="comment">/* to this parent.  collapse tree at the same time */</span></div>
<div class="line"><a name="l01498"></a><span class="lineno"> 1498</span>&#160;      c = i ;</div>
<div class="line"><a name="l01499"></a><span class="lineno"> 1499</span>&#160;      <span class="comment">/* get order of parent */</span></div>
<div class="line"><a name="l01500"></a><span class="lineno"> 1500</span>&#160;      order = Col [parent].shared2.order ;</div>
<div class="line"><a name="l01501"></a><span class="lineno"> 1501</span>&#160; </div>
<div class="line"><a name="l01502"></a><span class="lineno"> 1502</span>&#160;      <span class="keywordflow">do</span></div>
<div class="line"><a name="l01503"></a><span class="lineno"> 1503</span>&#160;      {</div>
<div class="line"><a name="l01504"></a><span class="lineno"> 1504</span>&#160;        COLAMD_ASSERT (Col [c].shared2.order == Empty) ;</div>
<div class="line"><a name="l01505"></a><span class="lineno"> 1505</span>&#160; </div>
<div class="line"><a name="l01506"></a><span class="lineno"> 1506</span>&#160;        <span class="comment">/* order this column */</span></div>
<div class="line"><a name="l01507"></a><span class="lineno"> 1507</span>&#160;        Col [c].shared2.order = order++ ;</div>
<div class="line"><a name="l01508"></a><span class="lineno"> 1508</span>&#160;        <span class="comment">/* collaps tree */</span></div>
<div class="line"><a name="l01509"></a><span class="lineno"> 1509</span>&#160;        Col [c].shared1.parent = parent ;</div>
<div class="line"><a name="l01510"></a><span class="lineno"> 1510</span>&#160; </div>
<div class="line"><a name="l01511"></a><span class="lineno"> 1511</span>&#160;        <span class="comment">/* get immediate parent of this column */</span></div>
<div class="line"><a name="l01512"></a><span class="lineno"> 1512</span>&#160;        c = Col [c].shared1.parent ;</div>
<div class="line"><a name="l01513"></a><span class="lineno"> 1513</span>&#160; </div>
<div class="line"><a name="l01514"></a><span class="lineno"> 1514</span>&#160;        <span class="comment">/* continue until we hit an ordered column.  There are */</span></div>
<div class="line"><a name="l01515"></a><span class="lineno"> 1515</span>&#160;        <span class="comment">/* guaranteed not to be anymore unordered columns */</span></div>
<div class="line"><a name="l01516"></a><span class="lineno"> 1516</span>&#160;        <span class="comment">/* above an ordered column */</span></div>
<div class="line"><a name="l01517"></a><span class="lineno"> 1517</span>&#160;      } <span class="keywordflow">while</span> (Col [c].shared2.order == Empty) ;</div>
<div class="line"><a name="l01518"></a><span class="lineno"> 1518</span>&#160; </div>
<div class="line"><a name="l01519"></a><span class="lineno"> 1519</span>&#160;      <span class="comment">/* re-order the super_col parent to largest order for this group */</span></div>
<div class="line"><a name="l01520"></a><span class="lineno"> 1520</span>&#160;      Col [parent].shared2.order = order ;</div>
<div class="line"><a name="l01521"></a><span class="lineno"> 1521</span>&#160;    }</div>
<div class="line"><a name="l01522"></a><span class="lineno"> 1522</span>&#160;  }</div>
<div class="line"><a name="l01523"></a><span class="lineno"> 1523</span>&#160; </div>
<div class="line"><a name="l01524"></a><span class="lineno"> 1524</span>&#160;  <span class="comment">/* === Generate the permutation ========================================= */</span></div>
<div class="line"><a name="l01525"></a><span class="lineno"> 1525</span>&#160; </div>
<div class="line"><a name="l01526"></a><span class="lineno"> 1526</span>&#160;  <span class="keywordflow">for</span> (c = 0 ; c &lt; n_col ; c++)</div>
<div class="line"><a name="l01527"></a><span class="lineno"> 1527</span>&#160;  {</div>
<div class="line"><a name="l01528"></a><span class="lineno"> 1528</span>&#160;    p [Col [c].shared2.order] = c ;</div>
<div class="line"><a name="l01529"></a><span class="lineno"> 1529</span>&#160;  }</div>
<div class="line"><a name="l01530"></a><span class="lineno"> 1530</span>&#160;}</div>
<div class="line"><a name="l01531"></a><span class="lineno"> 1531</span>&#160; </div>
<div class="line"><a name="l01532"></a><span class="lineno"> 1532</span>&#160; </div>
<div class="line"><a name="l01533"></a><span class="lineno"> 1533</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01534"></a><span class="lineno"> 1534</span>&#160;<span class="comment">/* === detect_super_cols ==================================================== */</span></div>
<div class="line"><a name="l01535"></a><span class="lineno"> 1535</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01536"></a><span class="lineno"> 1536</span>&#160; </div>
<div class="line"><a name="l01537"></a><span class="lineno"> 1537</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l01538"></a><span class="lineno"> 1538</span>&#160;<span class="comment">  Detects supercolumns by finding matches between columns in the hash buckets.</span></div>
<div class="line"><a name="l01539"></a><span class="lineno"> 1539</span>&#160;<span class="comment">  Check amongst columns in the set A [row_start ... row_start + row_length-1].</span></div>
<div class="line"><a name="l01540"></a><span class="lineno"> 1540</span>&#160;<span class="comment">  The columns under consideration are currently *not* in the degree lists,</span></div>
<div class="line"><a name="l01541"></a><span class="lineno"> 1541</span>&#160;<span class="comment">  and have already been placed in the hash buckets.</span></div>
<div class="line"><a name="l01542"></a><span class="lineno"> 1542</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l01543"></a><span class="lineno"> 1543</span>&#160;<span class="comment">  The hash bucket for columns whose hash function is equal to h is stored</span></div>
<div class="line"><a name="l01544"></a><span class="lineno"> 1544</span>&#160;<span class="comment">  as follows:</span></div>
<div class="line"><a name="l01545"></a><span class="lineno"> 1545</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l01546"></a><span class="lineno"> 1546</span>&#160;<span class="comment">  if head [h] is &gt;= 0, then head [h] contains a degree list, so:</span></div>
<div class="line"><a name="l01547"></a><span class="lineno"> 1547</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l01548"></a><span class="lineno"> 1548</span>&#160;<span class="comment">  head [h] is the first column in degree bucket h.</span></div>
<div class="line"><a name="l01549"></a><span class="lineno"> 1549</span>&#160;<span class="comment">  Col [head [h]].headhash gives the first column in hash bucket h.</span></div>
<div class="line"><a name="l01550"></a><span class="lineno"> 1550</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l01551"></a><span class="lineno"> 1551</span>&#160;<span class="comment">  otherwise, the degree list is empty, and:</span></div>
<div class="line"><a name="l01552"></a><span class="lineno"> 1552</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l01553"></a><span class="lineno"> 1553</span>&#160;<span class="comment">  -(head [h] + 2) is the first column in hash bucket h.</span></div>
<div class="line"><a name="l01554"></a><span class="lineno"> 1554</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l01555"></a><span class="lineno"> 1555</span>&#160;<span class="comment">  For a column c in a hash bucket, Col [c].shared3.prev is NOT a &quot;previous</span></div>
<div class="line"><a name="l01556"></a><span class="lineno"> 1556</span>&#160;<span class="comment">  column&quot; pointer.  Col [c].shared3.hash is used instead as the hash number</span></div>
<div class="line"><a name="l01557"></a><span class="lineno"> 1557</span>&#160;<span class="comment">  for that column.  The value of Col [c].shared4.hash_next is the next column</span></div>
<div class="line"><a name="l01558"></a><span class="lineno"> 1558</span>&#160;<span class="comment">  in the same hash bucket.</span></div>
<div class="line"><a name="l01559"></a><span class="lineno"> 1559</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l01560"></a><span class="lineno"> 1560</span>&#160;<span class="comment">  Assuming no, or &quot;few&quot; hash collisions, the time taken by this routine is</span></div>
<div class="line"><a name="l01561"></a><span class="lineno"> 1561</span>&#160;<span class="comment">  linear in the sum of the sizes (lengths) of each column whose score has</span></div>
<div class="line"><a name="l01562"></a><span class="lineno"> 1562</span>&#160;<span class="comment">  just been computed in the approximate degree computation.</span></div>
<div class="line"><a name="l01563"></a><span class="lineno"> 1563</span>&#160;<span class="comment">  Not user-callable.</span></div>
<div class="line"><a name="l01564"></a><span class="lineno"> 1564</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l01565"></a><span class="lineno"> 1565</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l01566"></a><span class="lineno"> 1566</span>&#160;<span class="keyword">static</span> <span class="keywordtype">void</span> detect_super_cols</div>
<div class="line"><a name="l01567"></a><span class="lineno"> 1567</span>&#160;(</div>
<div class="line"><a name="l01568"></a><span class="lineno"> 1568</span>&#160;  <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l01569"></a><span class="lineno"> 1569</span>&#160; </div>
<div class="line"><a name="l01570"></a><span class="lineno"> 1570</span>&#160;  ColStructure&lt;IndexType&gt; Col [],    <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l01571"></a><span class="lineno"> 1571</span>&#160;  IndexType A [],     <span class="comment">/* row indices of A */</span></div>
<div class="line"><a name="l01572"></a><span class="lineno"> 1572</span>&#160;  IndexType head [],    <span class="comment">/* head of degree lists and hash buckets */</span></div>
<div class="line"><a name="l01573"></a><span class="lineno"> 1573</span>&#160;  IndexType row_start,    <span class="comment">/* pointer to set of columns to check */</span></div>
<div class="line"><a name="l01574"></a><span class="lineno"> 1574</span>&#160;  IndexType row_length    <span class="comment">/* number of columns to check */</span></div>
<div class="line"><a name="l01575"></a><span class="lineno"> 1575</span>&#160;)</div>
<div class="line"><a name="l01576"></a><span class="lineno"> 1576</span>&#160;{</div>
<div class="line"><a name="l01577"></a><span class="lineno"> 1577</span>&#160;  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l01578"></a><span class="lineno"> 1578</span>&#160; </div>
<div class="line"><a name="l01579"></a><span class="lineno"> 1579</span>&#160;  IndexType hash ;      <span class="comment">/* hash value for a column */</span></div>
<div class="line"><a name="l01580"></a><span class="lineno"> 1580</span>&#160;  IndexType *rp ;     <span class="comment">/* pointer to a row */</span></div>
<div class="line"><a name="l01581"></a><span class="lineno"> 1581</span>&#160;  IndexType c ;     <span class="comment">/* a column index */</span></div>
<div class="line"><a name="l01582"></a><span class="lineno"> 1582</span>&#160;  IndexType super_c ;   <span class="comment">/* column index of the column to absorb into */</span></div>
<div class="line"><a name="l01583"></a><span class="lineno"> 1583</span>&#160;  IndexType *cp1 ;      <span class="comment">/* column pointer for column super_c */</span></div>
<div class="line"><a name="l01584"></a><span class="lineno"> 1584</span>&#160;  IndexType *cp2 ;      <span class="comment">/* column pointer for column c */</span></div>
<div class="line"><a name="l01585"></a><span class="lineno"> 1585</span>&#160;  IndexType length ;    <span class="comment">/* length of column super_c */</span></div>
<div class="line"><a name="l01586"></a><span class="lineno"> 1586</span>&#160;  IndexType prev_c ;    <span class="comment">/* column preceding c in hash bucket */</span></div>
<div class="line"><a name="l01587"></a><span class="lineno"> 1587</span>&#160;  IndexType i ;     <span class="comment">/* loop counter */</span></div>
<div class="line"><a name="l01588"></a><span class="lineno"> 1588</span>&#160;  IndexType *rp_end ;   <span class="comment">/* pointer to the end of the row */</span></div>
<div class="line"><a name="l01589"></a><span class="lineno"> 1589</span>&#160;  IndexType col ;     <span class="comment">/* a column index in the row to check */</span></div>
<div class="line"><a name="l01590"></a><span class="lineno"> 1590</span>&#160;  IndexType head_column ;   <span class="comment">/* first column in hash bucket or degree list */</span></div>
<div class="line"><a name="l01591"></a><span class="lineno"> 1591</span>&#160;  IndexType first_col ;   <span class="comment">/* first column in hash bucket */</span></div>
<div class="line"><a name="l01592"></a><span class="lineno"> 1592</span>&#160; </div>
<div class="line"><a name="l01593"></a><span class="lineno"> 1593</span>&#160;  <span class="comment">/* === Consider each column in the row ================================== */</span></div>
<div class="line"><a name="l01594"></a><span class="lineno"> 1594</span>&#160; </div>
<div class="line"><a name="l01595"></a><span class="lineno"> 1595</span>&#160;  rp = &amp;A [row_start] ;</div>
<div class="line"><a name="l01596"></a><span class="lineno"> 1596</span>&#160;  rp_end = rp + row_length ;</div>
<div class="line"><a name="l01597"></a><span class="lineno"> 1597</span>&#160;  <span class="keywordflow">while</span> (rp &lt; rp_end)</div>
<div class="line"><a name="l01598"></a><span class="lineno"> 1598</span>&#160;  {</div>
<div class="line"><a name="l01599"></a><span class="lineno"> 1599</span>&#160;    col = *rp++ ;</div>
<div class="line"><a name="l01600"></a><span class="lineno"> 1600</span>&#160;    <span class="keywordflow">if</span> (Col[col].is_dead())</div>
<div class="line"><a name="l01601"></a><span class="lineno"> 1601</span>&#160;    {</div>
<div class="line"><a name="l01602"></a><span class="lineno"> 1602</span>&#160;      continue ;</div>
<div class="line"><a name="l01603"></a><span class="lineno"> 1603</span>&#160;    }</div>
<div class="line"><a name="l01604"></a><span class="lineno"> 1604</span>&#160; </div>
<div class="line"><a name="l01605"></a><span class="lineno"> 1605</span>&#160;    <span class="comment">/* get hash number for this column */</span></div>
<div class="line"><a name="l01606"></a><span class="lineno"> 1606</span>&#160;    hash = Col [col].shared3.hash ;</div>
<div class="line"><a name="l01607"></a><span class="lineno"> 1607</span>&#160;    COLAMD_ASSERT (hash &lt;= n_col) ;</div>
<div class="line"><a name="l01608"></a><span class="lineno"> 1608</span>&#160; </div>
<div class="line"><a name="l01609"></a><span class="lineno"> 1609</span>&#160;    <span class="comment">/* === Get the first column in this hash bucket ===================== */</span></div>
<div class="line"><a name="l01610"></a><span class="lineno"> 1610</span>&#160; </div>
<div class="line"><a name="l01611"></a><span class="lineno"> 1611</span>&#160;    head_column = head [hash] ;</div>
<div class="line"><a name="l01612"></a><span class="lineno"> 1612</span>&#160;    <span class="keywordflow">if</span> (head_column &gt; Empty)</div>
<div class="line"><a name="l01613"></a><span class="lineno"> 1613</span>&#160;    {</div>
<div class="line"><a name="l01614"></a><span class="lineno"> 1614</span>&#160;      first_col = Col [head_column].shared3.headhash ;</div>
<div class="line"><a name="l01615"></a><span class="lineno"> 1615</span>&#160;    }</div>
<div class="line"><a name="l01616"></a><span class="lineno"> 1616</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l01617"></a><span class="lineno"> 1617</span>&#160;    {</div>
<div class="line"><a name="l01618"></a><span class="lineno"> 1618</span>&#160;      first_col = - (head_column + 2) ;</div>
<div class="line"><a name="l01619"></a><span class="lineno"> 1619</span>&#160;    }</div>
<div class="line"><a name="l01620"></a><span class="lineno"> 1620</span>&#160; </div>
<div class="line"><a name="l01621"></a><span class="lineno"> 1621</span>&#160;    <span class="comment">/* === Consider each column in the hash bucket ====================== */</span></div>
<div class="line"><a name="l01622"></a><span class="lineno"> 1622</span>&#160; </div>
<div class="line"><a name="l01623"></a><span class="lineno"> 1623</span>&#160;    <span class="keywordflow">for</span> (super_c = first_col ; super_c != Empty ;</div>
<div class="line"><a name="l01624"></a><span class="lineno"> 1624</span>&#160;         super_c = Col [super_c].shared4.hash_next)</div>
<div class="line"><a name="l01625"></a><span class="lineno"> 1625</span>&#160;    {</div>
<div class="line"><a name="l01626"></a><span class="lineno"> 1626</span>&#160;      COLAMD_ASSERT (Col [super_c].is_alive()) ;</div>
<div class="line"><a name="l01627"></a><span class="lineno"> 1627</span>&#160;      COLAMD_ASSERT (Col [super_c].shared3.hash == hash) ;</div>
<div class="line"><a name="l01628"></a><span class="lineno"> 1628</span>&#160;      length = Col [super_c].length ;</div>
<div class="line"><a name="l01629"></a><span class="lineno"> 1629</span>&#160; </div>
<div class="line"><a name="l01630"></a><span class="lineno"> 1630</span>&#160;      <span class="comment">/* prev_c is the column preceding column c in the hash bucket */</span></div>
<div class="line"><a name="l01631"></a><span class="lineno"> 1631</span>&#160;      prev_c = super_c ;</div>
<div class="line"><a name="l01632"></a><span class="lineno"> 1632</span>&#160; </div>
<div class="line"><a name="l01633"></a><span class="lineno"> 1633</span>&#160;      <span class="comment">/* === Compare super_c with all columns after it ================ */</span></div>
<div class="line"><a name="l01634"></a><span class="lineno"> 1634</span>&#160; </div>
<div class="line"><a name="l01635"></a><span class="lineno"> 1635</span>&#160;      <span class="keywordflow">for</span> (c = Col [super_c].shared4.hash_next ;</div>
<div class="line"><a name="l01636"></a><span class="lineno"> 1636</span>&#160;           c != Empty ; c = Col [c].shared4.hash_next)</div>
<div class="line"><a name="l01637"></a><span class="lineno"> 1637</span>&#160;      {</div>
<div class="line"><a name="l01638"></a><span class="lineno"> 1638</span>&#160;        COLAMD_ASSERT (c != super_c) ;</div>
<div class="line"><a name="l01639"></a><span class="lineno"> 1639</span>&#160;        COLAMD_ASSERT (Col[c].is_alive()) ;</div>
<div class="line"><a name="l01640"></a><span class="lineno"> 1640</span>&#160;        COLAMD_ASSERT (Col [c].shared3.hash == hash) ;</div>
<div class="line"><a name="l01641"></a><span class="lineno"> 1641</span>&#160; </div>
<div class="line"><a name="l01642"></a><span class="lineno"> 1642</span>&#160;        <span class="comment">/* not identical if lengths or scores are different */</span></div>
<div class="line"><a name="l01643"></a><span class="lineno"> 1643</span>&#160;        <span class="keywordflow">if</span> (Col [c].length != length ||</div>
<div class="line"><a name="l01644"></a><span class="lineno"> 1644</span>&#160;            Col [c].shared2.score != Col [super_c].shared2.score)</div>
<div class="line"><a name="l01645"></a><span class="lineno"> 1645</span>&#160;        {</div>
<div class="line"><a name="l01646"></a><span class="lineno"> 1646</span>&#160;          prev_c = c ;</div>
<div class="line"><a name="l01647"></a><span class="lineno"> 1647</span>&#160;          continue ;</div>
<div class="line"><a name="l01648"></a><span class="lineno"> 1648</span>&#160;        }</div>
<div class="line"><a name="l01649"></a><span class="lineno"> 1649</span>&#160; </div>
<div class="line"><a name="l01650"></a><span class="lineno"> 1650</span>&#160;        <span class="comment">/* compare the two columns */</span></div>
<div class="line"><a name="l01651"></a><span class="lineno"> 1651</span>&#160;        cp1 = &amp;A [Col [super_c].start] ;</div>
<div class="line"><a name="l01652"></a><span class="lineno"> 1652</span>&#160;        cp2 = &amp;A [Col [c].start] ;</div>
<div class="line"><a name="l01653"></a><span class="lineno"> 1653</span>&#160; </div>
<div class="line"><a name="l01654"></a><span class="lineno"> 1654</span>&#160;        <span class="keywordflow">for</span> (i = 0 ; i &lt; length ; i++)</div>
<div class="line"><a name="l01655"></a><span class="lineno"> 1655</span>&#160;        {</div>
<div class="line"><a name="l01656"></a><span class="lineno"> 1656</span>&#160;          <span class="comment">/* the columns are &quot;clean&quot; (no dead rows) */</span></div>
<div class="line"><a name="l01657"></a><span class="lineno"> 1657</span>&#160;          COLAMD_ASSERT ( cp1-&gt;is_alive() );</div>
<div class="line"><a name="l01658"></a><span class="lineno"> 1658</span>&#160;          COLAMD_ASSERT ( cp2-&gt;is_alive() );</div>
<div class="line"><a name="l01659"></a><span class="lineno"> 1659</span>&#160;          <span class="comment">/* row indices will same order for both supercols, */</span></div>
<div class="line"><a name="l01660"></a><span class="lineno"> 1660</span>&#160;          <span class="comment">/* no gather scatter necessary */</span></div>
<div class="line"><a name="l01661"></a><span class="lineno"> 1661</span>&#160;          <span class="keywordflow">if</span> (*cp1++ != *cp2++)</div>
<div class="line"><a name="l01662"></a><span class="lineno"> 1662</span>&#160;          {</div>
<div class="line"><a name="l01663"></a><span class="lineno"> 1663</span>&#160;            break ;</div>
<div class="line"><a name="l01664"></a><span class="lineno"> 1664</span>&#160;          }</div>
<div class="line"><a name="l01665"></a><span class="lineno"> 1665</span>&#160;        }</div>
<div class="line"><a name="l01666"></a><span class="lineno"> 1666</span>&#160; </div>
<div class="line"><a name="l01667"></a><span class="lineno"> 1667</span>&#160;        <span class="comment">/* the two columns are different if the for-loop &quot;broke&quot; */</span></div>
<div class="line"><a name="l01668"></a><span class="lineno"> 1668</span>&#160;        <span class="keywordflow">if</span> (i != length)</div>
<div class="line"><a name="l01669"></a><span class="lineno"> 1669</span>&#160;        {</div>
<div class="line"><a name="l01670"></a><span class="lineno"> 1670</span>&#160;          prev_c = c ;</div>
<div class="line"><a name="l01671"></a><span class="lineno"> 1671</span>&#160;          continue ;</div>
<div class="line"><a name="l01672"></a><span class="lineno"> 1672</span>&#160;        }</div>
<div class="line"><a name="l01673"></a><span class="lineno"> 1673</span>&#160; </div>
<div class="line"><a name="l01674"></a><span class="lineno"> 1674</span>&#160;        <span class="comment">/* === Got it!  two columns are identical =================== */</span></div>
<div class="line"><a name="l01675"></a><span class="lineno"> 1675</span>&#160; </div>
<div class="line"><a name="l01676"></a><span class="lineno"> 1676</span>&#160;        COLAMD_ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ;</div>
<div class="line"><a name="l01677"></a><span class="lineno"> 1677</span>&#160; </div>
<div class="line"><a name="l01678"></a><span class="lineno"> 1678</span>&#160;        Col [super_c].shared1.thickness += Col [c].shared1.thickness ;</div>
<div class="line"><a name="l01679"></a><span class="lineno"> 1679</span>&#160;        Col [c].shared1.parent = super_c ;</div>
<div class="line"><a name="l01680"></a><span class="lineno"> 1680</span>&#160;        Col[c].kill_non_principal() ;</div>
<div class="line"><a name="l01681"></a><span class="lineno"> 1681</span>&#160;        <span class="comment">/* order c later, in order_children() */</span></div>
<div class="line"><a name="l01682"></a><span class="lineno"> 1682</span>&#160;        Col [c].shared2.order = Empty ;</div>
<div class="line"><a name="l01683"></a><span class="lineno"> 1683</span>&#160;        <span class="comment">/* remove c from hash bucket */</span></div>
<div class="line"><a name="l01684"></a><span class="lineno"> 1684</span>&#160;        Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ;</div>
<div class="line"><a name="l01685"></a><span class="lineno"> 1685</span>&#160;      }</div>
<div class="line"><a name="l01686"></a><span class="lineno"> 1686</span>&#160;    }</div>
<div class="line"><a name="l01687"></a><span class="lineno"> 1687</span>&#160; </div>
<div class="line"><a name="l01688"></a><span class="lineno"> 1688</span>&#160;    <span class="comment">/* === Empty this hash bucket ======================================= */</span></div>
<div class="line"><a name="l01689"></a><span class="lineno"> 1689</span>&#160; </div>
<div class="line"><a name="l01690"></a><span class="lineno"> 1690</span>&#160;    <span class="keywordflow">if</span> (head_column &gt; Empty)</div>
<div class="line"><a name="l01691"></a><span class="lineno"> 1691</span>&#160;    {</div>
<div class="line"><a name="l01692"></a><span class="lineno"> 1692</span>&#160;      <span class="comment">/* corresponding degree list &quot;hash&quot; is not empty */</span></div>
<div class="line"><a name="l01693"></a><span class="lineno"> 1693</span>&#160;      Col [head_column].shared3.headhash = Empty ;</div>
<div class="line"><a name="l01694"></a><span class="lineno"> 1694</span>&#160;    }</div>
<div class="line"><a name="l01695"></a><span class="lineno"> 1695</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l01696"></a><span class="lineno"> 1696</span>&#160;    {</div>
<div class="line"><a name="l01697"></a><span class="lineno"> 1697</span>&#160;      <span class="comment">/* corresponding degree list &quot;hash&quot; is empty */</span></div>
<div class="line"><a name="l01698"></a><span class="lineno"> 1698</span>&#160;      head [hash] = Empty ;</div>
<div class="line"><a name="l01699"></a><span class="lineno"> 1699</span>&#160;    }</div>
<div class="line"><a name="l01700"></a><span class="lineno"> 1700</span>&#160;  }</div>
<div class="line"><a name="l01701"></a><span class="lineno"> 1701</span>&#160;}</div>
<div class="line"><a name="l01702"></a><span class="lineno"> 1702</span>&#160; </div>
<div class="line"><a name="l01703"></a><span class="lineno"> 1703</span>&#160; </div>
<div class="line"><a name="l01704"></a><span class="lineno"> 1704</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01705"></a><span class="lineno"> 1705</span>&#160;<span class="comment">/* === garbage_collection =================================================== */</span></div>
<div class="line"><a name="l01706"></a><span class="lineno"> 1706</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01707"></a><span class="lineno"> 1707</span>&#160; </div>
<div class="line"><a name="l01708"></a><span class="lineno"> 1708</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l01709"></a><span class="lineno"> 1709</span>&#160;<span class="comment">  Defragments and compacts columns and rows in the workspace A.  Used when</span></div>
<div class="line"><a name="l01710"></a><span class="lineno"> 1710</span>&#160;<span class="comment">  all available memory has been used while performing row merging.  Returns</span></div>
<div class="line"><a name="l01711"></a><span class="lineno"> 1711</span>&#160;<span class="comment">  the index of the first free position in A, after garbage collection.  The</span></div>
<div class="line"><a name="l01712"></a><span class="lineno"> 1712</span>&#160;<span class="comment">  time taken by this routine is linear is the size of the array A, which is</span></div>
<div class="line"><a name="l01713"></a><span class="lineno"> 1713</span>&#160;<span class="comment">  itself linear in the number of nonzeros in the input matrix.</span></div>
<div class="line"><a name="l01714"></a><span class="lineno"> 1714</span>&#160;<span class="comment">  Not user-callable.</span></div>
<div class="line"><a name="l01715"></a><span class="lineno"> 1715</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l01716"></a><span class="lineno"> 1716</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l01717"></a><span class="lineno"> 1717</span>&#160;<span class="keyword">static</span> IndexType garbage_collection  <span class="comment">/* returns the new value of pfree */</span></div>
<div class="line"><a name="l01718"></a><span class="lineno"> 1718</span>&#160;  (</div>
<div class="line"><a name="l01719"></a><span class="lineno"> 1719</span>&#160;    <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l01720"></a><span class="lineno"> 1720</span>&#160; </div>
<div class="line"><a name="l01721"></a><span class="lineno"> 1721</span>&#160;    IndexType n_row,      <span class="comment">/* number of rows */</span></div>
<div class="line"><a name="l01722"></a><span class="lineno"> 1722</span>&#160;    IndexType n_col,      <span class="comment">/* number of columns */</span></div>
<div class="line"><a name="l01723"></a><span class="lineno"> 1723</span>&#160;    RowStructure&lt;IndexType&gt; Row [],    <span class="comment">/* row info */</span></div>
<div class="line"><a name="l01724"></a><span class="lineno"> 1724</span>&#160;    ColStructure&lt;IndexType&gt; Col [],    <span class="comment">/* column info */</span></div>
<div class="line"><a name="l01725"></a><span class="lineno"> 1725</span>&#160;    IndexType A [],     <span class="comment">/* A [0 ... Alen-1] holds the matrix */</span></div>
<div class="line"><a name="l01726"></a><span class="lineno"> 1726</span>&#160;    IndexType *pfree      <span class="comment">/* &amp;A [0] ... pfree is in use */</span></div>
<div class="line"><a name="l01727"></a><span class="lineno"> 1727</span>&#160;    )</div>
<div class="line"><a name="l01728"></a><span class="lineno"> 1728</span>&#160;{</div>
<div class="line"><a name="l01729"></a><span class="lineno"> 1729</span>&#160;  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l01730"></a><span class="lineno"> 1730</span>&#160; </div>
<div class="line"><a name="l01731"></a><span class="lineno"> 1731</span>&#160;  IndexType *psrc ;     <span class="comment">/* source pointer */</span></div>
<div class="line"><a name="l01732"></a><span class="lineno"> 1732</span>&#160;  IndexType *pdest ;    <span class="comment">/* destination pointer */</span></div>
<div class="line"><a name="l01733"></a><span class="lineno"> 1733</span>&#160;  IndexType j ;     <span class="comment">/* counter */</span></div>
<div class="line"><a name="l01734"></a><span class="lineno"> 1734</span>&#160;  IndexType r ;     <span class="comment">/* a row index */</span></div>
<div class="line"><a name="l01735"></a><span class="lineno"> 1735</span>&#160;  IndexType c ;     <span class="comment">/* a column index */</span></div>
<div class="line"><a name="l01736"></a><span class="lineno"> 1736</span>&#160;  IndexType length ;    <span class="comment">/* length of a row or column */</span></div>
<div class="line"><a name="l01737"></a><span class="lineno"> 1737</span>&#160; </div>
<div class="line"><a name="l01738"></a><span class="lineno"> 1738</span>&#160;  <span class="comment">/* === Defragment the columns =========================================== */</span></div>
<div class="line"><a name="l01739"></a><span class="lineno"> 1739</span>&#160; </div>
<div class="line"><a name="l01740"></a><span class="lineno"> 1740</span>&#160;  pdest = &amp;A[0] ;</div>
<div class="line"><a name="l01741"></a><span class="lineno"> 1741</span>&#160;  <span class="keywordflow">for</span> (c = 0 ; c &lt; n_col ; c++)</div>
<div class="line"><a name="l01742"></a><span class="lineno"> 1742</span>&#160;  {</div>
<div class="line"><a name="l01743"></a><span class="lineno"> 1743</span>&#160;    <span class="keywordflow">if</span> (Col[c].is_alive())</div>
<div class="line"><a name="l01744"></a><span class="lineno"> 1744</span>&#160;    {</div>
<div class="line"><a name="l01745"></a><span class="lineno"> 1745</span>&#160;      psrc = &amp;A [Col [c].start] ;</div>
<div class="line"><a name="l01746"></a><span class="lineno"> 1746</span>&#160; </div>
<div class="line"><a name="l01747"></a><span class="lineno"> 1747</span>&#160;      <span class="comment">/* move and compact the column */</span></div>
<div class="line"><a name="l01748"></a><span class="lineno"> 1748</span>&#160;      COLAMD_ASSERT (pdest &lt;= psrc) ;</div>
<div class="line"><a name="l01749"></a><span class="lineno"> 1749</span>&#160;      Col [c].start = (IndexType) (pdest - &amp;A [0]) ;</div>
<div class="line"><a name="l01750"></a><span class="lineno"> 1750</span>&#160;      length = Col [c].length ;</div>
<div class="line"><a name="l01751"></a><span class="lineno"> 1751</span>&#160;      <span class="keywordflow">for</span> (j = 0 ; j &lt; length ; j++)</div>
<div class="line"><a name="l01752"></a><span class="lineno"> 1752</span>&#160;      {</div>
<div class="line"><a name="l01753"></a><span class="lineno"> 1753</span>&#160;        r = *psrc++ ;</div>
<div class="line"><a name="l01754"></a><span class="lineno"> 1754</span>&#160;        <span class="keywordflow">if</span> (Row[r].is_alive())</div>
<div class="line"><a name="l01755"></a><span class="lineno"> 1755</span>&#160;        {</div>
<div class="line"><a name="l01756"></a><span class="lineno"> 1756</span>&#160;          *pdest++ = r ;</div>
<div class="line"><a name="l01757"></a><span class="lineno"> 1757</span>&#160;        }</div>
<div class="line"><a name="l01758"></a><span class="lineno"> 1758</span>&#160;      }</div>
<div class="line"><a name="l01759"></a><span class="lineno"> 1759</span>&#160;      Col [c].length = (IndexType) (pdest - &amp;A [Col [c].start]) ;</div>
<div class="line"><a name="l01760"></a><span class="lineno"> 1760</span>&#160;    }</div>
<div class="line"><a name="l01761"></a><span class="lineno"> 1761</span>&#160;  }</div>
<div class="line"><a name="l01762"></a><span class="lineno"> 1762</span>&#160; </div>
<div class="line"><a name="l01763"></a><span class="lineno"> 1763</span>&#160;  <span class="comment">/* === Prepare to defragment the rows =================================== */</span></div>
<div class="line"><a name="l01764"></a><span class="lineno"> 1764</span>&#160; </div>
<div class="line"><a name="l01765"></a><span class="lineno"> 1765</span>&#160;  <span class="keywordflow">for</span> (r = 0 ; r &lt; n_row ; r++)</div>
<div class="line"><a name="l01766"></a><span class="lineno"> 1766</span>&#160;  {</div>
<div class="line"><a name="l01767"></a><span class="lineno"> 1767</span>&#160;    <span class="keywordflow">if</span> (Row[r].is_alive())</div>
<div class="line"><a name="l01768"></a><span class="lineno"> 1768</span>&#160;    {</div>
<div class="line"><a name="l01769"></a><span class="lineno"> 1769</span>&#160;      <span class="keywordflow">if</span> (Row [r].length == 0)</div>
<div class="line"><a name="l01770"></a><span class="lineno"> 1770</span>&#160;      {</div>
<div class="line"><a name="l01771"></a><span class="lineno"> 1771</span>&#160;        <span class="comment">/* this row is of zero length.  cannot compact it, so kill it */</span></div>
<div class="line"><a name="l01772"></a><span class="lineno"> 1772</span>&#160;        COLAMD_DEBUG3 ((<span class="stringliteral">&quot;Defrag row kill\n&quot;</span>)) ;</div>
<div class="line"><a name="l01773"></a><span class="lineno"> 1773</span>&#160;        Row[r].kill() ;</div>
<div class="line"><a name="l01774"></a><span class="lineno"> 1774</span>&#160;      }</div>
<div class="line"><a name="l01775"></a><span class="lineno"> 1775</span>&#160;      <span class="keywordflow">else</span></div>
<div class="line"><a name="l01776"></a><span class="lineno"> 1776</span>&#160;      {</div>
<div class="line"><a name="l01777"></a><span class="lineno"> 1777</span>&#160;        <span class="comment">/* save first column index in Row [r].shared2.first_column */</span></div>
<div class="line"><a name="l01778"></a><span class="lineno"> 1778</span>&#160;        psrc = &amp;A [Row [r].start] ;</div>
<div class="line"><a name="l01779"></a><span class="lineno"> 1779</span>&#160;        Row [r].shared2.first_column = *psrc ;</div>
<div class="line"><a name="l01780"></a><span class="lineno"> 1780</span>&#160;        COLAMD_ASSERT (Row[r].is_alive()) ;</div>
<div class="line"><a name="l01781"></a><span class="lineno"> 1781</span>&#160;        <span class="comment">/* flag the start of the row with the one&#39;s complement of row */</span></div>
<div class="line"><a name="l01782"></a><span class="lineno"> 1782</span>&#160;        *psrc = ones_complement(r) ;</div>
<div class="line"><a name="l01783"></a><span class="lineno"> 1783</span>&#160; </div>
<div class="line"><a name="l01784"></a><span class="lineno"> 1784</span>&#160;      }</div>
<div class="line"><a name="l01785"></a><span class="lineno"> 1785</span>&#160;    }</div>
<div class="line"><a name="l01786"></a><span class="lineno"> 1786</span>&#160;  }</div>
<div class="line"><a name="l01787"></a><span class="lineno"> 1787</span>&#160; </div>
<div class="line"><a name="l01788"></a><span class="lineno"> 1788</span>&#160;  <span class="comment">/* === Defragment the rows ============================================== */</span></div>
<div class="line"><a name="l01789"></a><span class="lineno"> 1789</span>&#160; </div>
<div class="line"><a name="l01790"></a><span class="lineno"> 1790</span>&#160;  psrc = pdest ;</div>
<div class="line"><a name="l01791"></a><span class="lineno"> 1791</span>&#160;  <span class="keywordflow">while</span> (psrc &lt; pfree)</div>
<div class="line"><a name="l01792"></a><span class="lineno"> 1792</span>&#160;  {</div>
<div class="line"><a name="l01793"></a><span class="lineno"> 1793</span>&#160;    <span class="comment">/* find a negative number ... the start of a row */</span></div>
<div class="line"><a name="l01794"></a><span class="lineno"> 1794</span>&#160;    <span class="keywordflow">if</span> (*psrc++ &lt; 0)</div>
<div class="line"><a name="l01795"></a><span class="lineno"> 1795</span>&#160;    {</div>
<div class="line"><a name="l01796"></a><span class="lineno"> 1796</span>&#160;      psrc-- ;</div>
<div class="line"><a name="l01797"></a><span class="lineno"> 1797</span>&#160;      <span class="comment">/* get the row index */</span></div>
<div class="line"><a name="l01798"></a><span class="lineno"> 1798</span>&#160;      r = ones_complement(*psrc) ;</div>
<div class="line"><a name="l01799"></a><span class="lineno"> 1799</span>&#160;      COLAMD_ASSERT (r &gt;= 0 &amp;&amp; r &lt; n_row) ;</div>
<div class="line"><a name="l01800"></a><span class="lineno"> 1800</span>&#160;      <span class="comment">/* restore first column index */</span></div>
<div class="line"><a name="l01801"></a><span class="lineno"> 1801</span>&#160;      *psrc = Row [r].shared2.first_column ;</div>
<div class="line"><a name="l01802"></a><span class="lineno"> 1802</span>&#160;      COLAMD_ASSERT (Row[r].is_alive()) ;</div>
<div class="line"><a name="l01803"></a><span class="lineno"> 1803</span>&#160; </div>
<div class="line"><a name="l01804"></a><span class="lineno"> 1804</span>&#160;      <span class="comment">/* move and compact the row */</span></div>
<div class="line"><a name="l01805"></a><span class="lineno"> 1805</span>&#160;      COLAMD_ASSERT (pdest &lt;= psrc) ;</div>
<div class="line"><a name="l01806"></a><span class="lineno"> 1806</span>&#160;      Row [r].start = (IndexType) (pdest - &amp;A [0]) ;</div>
<div class="line"><a name="l01807"></a><span class="lineno"> 1807</span>&#160;      length = Row [r].length ;</div>
<div class="line"><a name="l01808"></a><span class="lineno"> 1808</span>&#160;      <span class="keywordflow">for</span> (j = 0 ; j &lt; length ; j++)</div>
<div class="line"><a name="l01809"></a><span class="lineno"> 1809</span>&#160;      {</div>
<div class="line"><a name="l01810"></a><span class="lineno"> 1810</span>&#160;        c = *psrc++ ;</div>
<div class="line"><a name="l01811"></a><span class="lineno"> 1811</span>&#160;        <span class="keywordflow">if</span> (Col[c].is_alive())</div>
<div class="line"><a name="l01812"></a><span class="lineno"> 1812</span>&#160;        {</div>
<div class="line"><a name="l01813"></a><span class="lineno"> 1813</span>&#160;          *pdest++ = c ;</div>
<div class="line"><a name="l01814"></a><span class="lineno"> 1814</span>&#160;        }</div>
<div class="line"><a name="l01815"></a><span class="lineno"> 1815</span>&#160;      }</div>
<div class="line"><a name="l01816"></a><span class="lineno"> 1816</span>&#160;      Row [r].length = (IndexType) (pdest - &amp;A [Row [r].start]) ;</div>
<div class="line"><a name="l01817"></a><span class="lineno"> 1817</span>&#160; </div>
<div class="line"><a name="l01818"></a><span class="lineno"> 1818</span>&#160;    }</div>
<div class="line"><a name="l01819"></a><span class="lineno"> 1819</span>&#160;  }</div>
<div class="line"><a name="l01820"></a><span class="lineno"> 1820</span>&#160;  <span class="comment">/* ensure we found all the rows */</span></div>
<div class="line"><a name="l01821"></a><span class="lineno"> 1821</span>&#160;  COLAMD_ASSERT (debug_rows == 0) ;</div>
<div class="line"><a name="l01822"></a><span class="lineno"> 1822</span>&#160; </div>
<div class="line"><a name="l01823"></a><span class="lineno"> 1823</span>&#160;  <span class="comment">/* === Return the new value of pfree ==================================== */</span></div>
<div class="line"><a name="l01824"></a><span class="lineno"> 1824</span>&#160; </div>
<div class="line"><a name="l01825"></a><span class="lineno"> 1825</span>&#160;  <span class="keywordflow">return</span> ((IndexType) (pdest - &amp;A [0])) ;</div>
<div class="line"><a name="l01826"></a><span class="lineno"> 1826</span>&#160;}</div>
<div class="line"><a name="l01827"></a><span class="lineno"> 1827</span>&#160; </div>
<div class="line"><a name="l01828"></a><span class="lineno"> 1828</span>&#160; </div>
<div class="line"><a name="l01829"></a><span class="lineno"> 1829</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01830"></a><span class="lineno"> 1830</span>&#160;<span class="comment">/* === clear_mark =========================================================== */</span></div>
<div class="line"><a name="l01831"></a><span class="lineno"> 1831</span>&#160;<span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01832"></a><span class="lineno"> 1832</span>&#160; </div>
<div class="line"><a name="l01833"></a><span class="lineno"> 1833</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l01834"></a><span class="lineno"> 1834</span>&#160;<span class="comment">  Clears the Row [].shared2.mark array, and returns the new tag_mark.</span></div>
<div class="line"><a name="l01835"></a><span class="lineno"> 1835</span>&#160;<span class="comment">  Return value is the new tag_mark.  Not user-callable.</span></div>
<div class="line"><a name="l01836"></a><span class="lineno"> 1836</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l01837"></a><span class="lineno"> 1837</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> IndexType&gt;</div>
<div class="line"><a name="l01838"></a><span class="lineno"> 1838</span>&#160;<span class="keyword">static</span> <span class="keyword">inline</span>  IndexType clear_mark  <span class="comment">/* return the new value for tag_mark */</span></div>
<div class="line"><a name="l01839"></a><span class="lineno"> 1839</span>&#160;  (</div>
<div class="line"><a name="l01840"></a><span class="lineno"> 1840</span>&#160;      <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l01841"></a><span class="lineno"> 1841</span>&#160; </div>
<div class="line"><a name="l01842"></a><span class="lineno"> 1842</span>&#160;    IndexType n_row,    <span class="comment">/* number of rows in A */</span></div>
<div class="line"><a name="l01843"></a><span class="lineno"> 1843</span>&#160;    RowStructure&lt;IndexType&gt; Row [] <span class="comment">/* Row [0 ... n_row-1].shared2.mark is set to zero */</span></div>
<div class="line"><a name="l01844"></a><span class="lineno"> 1844</span>&#160;    )</div>
<div class="line"><a name="l01845"></a><span class="lineno"> 1845</span>&#160;{</div>
<div class="line"><a name="l01846"></a><span class="lineno"> 1846</span>&#160;  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l01847"></a><span class="lineno"> 1847</span>&#160; </div>
<div class="line"><a name="l01848"></a><span class="lineno"> 1848</span>&#160;  IndexType r ;</div>
<div class="line"><a name="l01849"></a><span class="lineno"> 1849</span>&#160; </div>
<div class="line"><a name="l01850"></a><span class="lineno"> 1850</span>&#160;  <span class="keywordflow">for</span> (r = 0 ; r &lt; n_row ; r++)</div>
<div class="line"><a name="l01851"></a><span class="lineno"> 1851</span>&#160;  {</div>
<div class="line"><a name="l01852"></a><span class="lineno"> 1852</span>&#160;    <span class="keywordflow">if</span> (Row[r].is_alive())</div>
<div class="line"><a name="l01853"></a><span class="lineno"> 1853</span>&#160;    {</div>
<div class="line"><a name="l01854"></a><span class="lineno"> 1854</span>&#160;      Row [r].shared2.mark = 0 ;</div>
<div class="line"><a name="l01855"></a><span class="lineno"> 1855</span>&#160;    }</div>
<div class="line"><a name="l01856"></a><span class="lineno"> 1856</span>&#160;  }</div>
<div class="line"><a name="l01857"></a><span class="lineno"> 1857</span>&#160;  <span class="keywordflow">return</span> (1) ;</div>
<div class="line"><a name="l01858"></a><span class="lineno"> 1858</span>&#160;}</div>
<div class="line"><a name="l01859"></a><span class="lineno"> 1859</span>&#160; </div>
<div class="line"><a name="l01860"></a><span class="lineno"> 1860</span>&#160;} <span class="comment">// namespace Colamd</span></div>
<div class="line"><a name="l01861"></a><span class="lineno"> 1861</span>&#160; </div>
<div class="line"><a name="l01862"></a><span class="lineno"> 1862</span>&#160;} <span class="comment">// namespace internal</span></div>
<div class="line"><a name="l01863"></a><span class="lineno"> 1863</span>&#160;<span class="preprocessor">#endif</span></div>
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